Saturday, December 17, 2011

How do you determine whether a line is parallel to a plane?

Linear Algebra question:





How do you determine whether a line is parallel to a plane?








How do I figure out whether this line is parallel to the following plane or not?





Line:


x = 3t


y = 1 +2t


z = 2-t





Plane:





4x-y+2z = 1





Thanks in advance.|||If the line and a normal vector of the plane are orthogonal then the line and the plane are parallel.





one normal vector to the plane is : v (4 ; - 1 ; 2)





one vector of the line is (3 ; 2 ; - 1)








scalar product of the two vectors =





(4 * 3) + ((- 1) * 2) + (2 * (- 1)) =





12 - 2 - 2 = 8





The result is not equal to 0 so the line and the plane are secant (not parallel).








Graph :





http://s636.photobucket.com/albums/uu88/鈥?/a>





*******|||If the directional vector of the line is orthogonal to the normal vector of the plane, the line and the plane are parallel. The dot product of orthogonal vectors is zero.





Let


v = directional vector of line


n = normal vector of plane





v = %26lt;3, 2, -1%26gt;


n = %26lt;4, -1, 2%26gt;





Take the dot product.


v 鈥?n = %26lt;3, 2, -1%26gt; 鈥?%26lt;4, -1, 2%26gt; = 12 - 2 - 2 = 8 鈮?0





The dot product is not zero, so the line and plane are not parallel.

What would be the most offensive thing to eat on a plane?

This question came up because my husband was mentioning how much he loves Maui onion chips. Then the thought crossed my mind why don't they serve these chips on the flights to Hawaii? I soon realized that everyone on the plane would end up having horrid breath and the following passengers would be welcomed with a plane scented with a wonderful perfume of Maui onion. So I began to wonder which other snacks or meals would not be a wise choice to consume on a plane.|||Durian Fruit|||i wouldnt want someone eating a tuna sandwich next to me... or anything that was wicked loud and crunchy|||anything w/fish or really smelly cheese|||cookies with "offensive weapons" in icing on them..

What are the statistics about fatal plane crashes within the United States?

I'm talking about plane crashes on major airlines, not like a private jet or anything like that. I'm referring to like a Jet Blue or Delta flight, and I'm only asking about flights within the continental USA, like from New York to Nevada or something like that. I've heard that the stats are 1 in a million but that sounds like it might just be hyperbolic.


Thanks.|||1 in a million is _not_ hyperbolic. There are lots of ways of expressing the risk, and that is one way. Regardless, flying if by far the safest way to travel.





You can find tons of data from the NTSB, specifically:





http://www.ntsb.gov/aviation/Table6.htm


Summary of accidents for US carriers from 1991, includes # of accidents, # of fatalities, # of flights, miles and hours flown.





Also:


http://www.ntsb.gov/aviationquery/index.鈥?/a>


Which is a searchable data base of accidents. You can specify date ranges, locations (country or down to the state/city level), airline, type of aircraft, commercial, private, scheduled and so on.





In the past 9 1/2 years (from 2002 to the present), there have been a total of 9 crashes with fatalities, in which a total of 157 people died. During that same time period (through the end of 2010), there have been more than:


. . . . 60,959,251 hours flown


67,639,054,000 miles flown


. . . .92,786,070 departures





Since about 100 people die from vehicle accidents in the US %26lt;every day%26gt;, during the same period of time, about 345,000 people have been killed in auto accidents.





It is pretty obvious which method of travel is safer.|||There hasn't been a crash by a major airline since 2009 and most major airlines in the US haven't had a fatal crash since many years before that. JetBlue has never had a fatal crash and Delta since 2006. I don't know the exact odds, but considering the number of flights in the US, your numbers probably aren't too far off. You can check stats here:


http://www.airsafe.com/airline.htm

How do I find out which plane Im flying on using Cathay Pacific?

I need to get onto the online checkin and get a seat prompty tomorrow. I am very tall so it would help to see a plan of the plane. Does anyone know how to find out which make of airline Cathay Pacific will using for their London-Melbourne flights?|||Run a search on www.cathaypacific.com and take a look at the aircraft identifier next to the flight. I'm going to guess that both segments will be operated by a Boeing 747 (you will need to connect in Hong Kong), since both are relatively high-density long-haul routes.





Anyways...


744, 74A - Boeing 747-400


772, 773 - Boeing 777-200, Boeing 777-300


330 - Airbus A330-300 (I think)


340 - Airbus A340-300


EQV - Equipment varies on different days.|||It usually will say on the schedule and your itinerary (e-ticket) what type of aircrafts, but for those long distance flights, it will most likely be either a Boeing 747, Airbus A330 or A340 cuz those type of aircraft have longer range.





check your email. they should have sent you a confirmation email with the flight information on there and the type of aircraft should be on there as well.|||You will be flying in either a 747 or Airubs 340 depending on what time your flight is. Then you will use an Airbus 330 to Melbourne from Hong Kong.





http://www.cathaypacific.com/cpa/en_INTL鈥?/a>





Go to http://www.seatguru.com to find what is a good seat and which ones to avoid.|||Any will fit you,Dont worry about that, man

What does it mean when you dream about flying in a plane?

I dreamt that I was going to NY in a plane. A lot happened but what stands out most is that my best friend's father who recently died was flying the plane. He came over, sat next to me and I asked if he was the pilot. He said yes, then started reading a newspaper. He told me he was taking a break. The plane was on autopilot now. Then he got up and said his break was over and he had to go back to work.|||sometimes it might mean you want to get away. But that your friends fathers dad who is dead is flying the airplane sometimes its the sadness you keep in your heart not only for yourself but mostly for her family|||If you are flying with ease and enjoying the scene and landscape below, then it suggests that you are on top of a situation. You have risen above something. It may also mean that you have gained a different perspective on things. Flying dreams and the ability to control your flight is representative of your own personal sense of power.





To see and talk with your dead parents(or friends parents) in your dreams, represents your fears of losing them or your way of coping with the loss. You may want that last opportunity to say your final good-byes to them.|||this was a spiritual dream (not in a religious form) in a inner insight of a person whom you knew in your past. flying means freedom and talking to dead people in you dreams but in a positive way like you did, means the person its letting you know they are in a better place and so will you. its sending you a message to let you know that their is a better place.|||well i will first answer the bit about your friends father:


This symbol is highly personalized, and should be considered in light of your relationship with your father. Generally, dreaming of a father (yours or anyone else's) represents authority, while mothers represent love and protection. If your relationship with your father was good, dreaming of him implies advancement and/or assistance from authority figures in your life. If your relationship with him was strained, however, dreaming of him indicates trouble coming from authority figures, such as your boss. If you're dreaming of a dead parent, especially if he or she is speaking to you, important news is coming your way. Whether the news is good or bad depends on other dynamics in the dream.


Ok so flying a plane i have three explanations:


1. Escape from the mundane exigencies of the lower world.


2. Freedom.


3. The search for higher consciousness. Travel into the higher realms.


and for the new york part:


The "hub of the world." 1. To be alone in New York City without any friends or companions is symbolic of being totally on your own. Whatever projects or enterprises you're facing right now are likely to have to be done almost entirely on your own.


2. The bright lights of New York City at night, especially if they blink on and off, symbolize an encouraging message that the solution to a problem you've been wrestling with will come to you in a bolt of inspiration.


3. Dreaming of hearing any of the vast number of songs about New York City represents reassurance that a cherished goal or project of yours will indeed manifest - with a lot of work.


ok so i hope you can piece together the information i gave you and hope it helps! if you need more information please got to the website below!

How closely inclined is the ecliptic plane to the solar equator?

And which planet is closest to the solar equatorial plane?|||Earth ecliptic is 7.155 deg.


Mercury is closest, followed by Venus.|||Also, kudos to "rich"





He answered the second part of my question how I phrased it, and not how I meant to (should have read, "which planets ORBIT is closest to the solar equatorial plane") sorry for that mixup.

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|||There is a seven degree inclination between the plane of the solar equator and the ecliptic. Mercury's orbit is inclined seven degrees to the eclipitc, but that doesn't put Mercury closest to the solar equatorial plane. It would depend on the sun's precession, and the planets' location in their orbits.|||Good question. I researched this a bit and have not come up with an answer.





Except to point out that neither the direction nor the magnitude of the Sun's angular momentum vector is well known, because the rotation of the material below the photosphere is not well known (although it can be investigated through solar seismology).





Jupiter's orbit is by far the biggest reservoir of angular momentum in the Solar System.





This website





http://www.valdostamuseum.org/hamsmith/a…





says that the sun's orbital momentum vector is tilted 7 degrees with respect to the sum of the planet's vectors.|||The ecliptic intersects the the celestial equator at two points: during the vernal equinox and autumnal equinox. This means that the ecliptic follows a circular path around the sky, half of the time above and half of the time below the celestial equator.|||The inclination is about 23.5 degrees - as for which one is close to being in the equatorial plane - I don't know - maybe one of the dwarf worlds?

What are the essentials to pack in a carry-on bag on a plane?

We are a family of first timers going on a plane to florida. What shall we bring in our carry-on bags? Also, what should my kids pack and bring? Ages 10 and 7.|||some form of entertainment. the plane will have a movie, but that cost some money and they might not show a movie you like. i would bring a CD player or mp3 or some form of music entertainment. Then a camera, that way you can take pictures of the clouds. some books or puzzle books, maybe coloring books/crayon for the kids.


water/snacks. after you go through the line where they check you for any metal [at the moment i forget what its called lol] there will be shops around there, and resteraunts. you can go to some of these shops and buy food, books, drinks, etc.


if you have one a portable DVD player. this way you can bring movies and watch them.


an extra pair of clothes just incase your luggage gets lost or you spill something on you.


maybe sometoys [not noisy ones] of your children's that they could play with. or a handheld video game.


gum is also good for ear popping when going up and down, plus its something to keep you occupied as weird as that sounds.





i would also sugest going to the airport around 1 1/2 hours-1hour ahead of time for check in, etc. and then about 10 or so minutes before they start loading go to the nearest bathroom, so you hopefully wont have to go on the plane.


once you first arrive at the airport[sorry this is out of order] give your big luggage [not carryons] to the nearest desk area that is where it gets checked in. remember to take your shoes off in the metal detection line too.





sry if it got confusing


have a great trip=]|||I like to bring some kind of entertainment (like music, a video game, etc). I would also bring some kind of snack for them to nibble on during the ride. Just make sure that you have something for them to do and something for them to snack on. You can't bring drinks, but you can still bring food.|||Honestly, to sit on one feels a bit like sitting on a bus. Until it starts moving. And then it still feels a bit like a bus, except faster. You'll know when you get off the ground because all of a sudden you can tell there isn't any friction under the wheels; it's really smooth. You gain altitude fairly quickly and you'll be able to tell you're leaning back a little. If you're brave enough/lucky enough to have a window seat, look out! It's so amazing to see the ground dropping away. Cars and trees go from looking normal sized to little dots so quickly. It might be a little rough as you gain altitude, but to me it's exciting. You might pass through clouds-- they look just like fog. And then all of a sudden, you're above the clouds looking down on them. It's so awesome!





As far as the flight attendants and such go, they'll go through the emergency procedures before you take off. Point to the exits, show the oxygen masks, etc. Just like in movies. They make sure all the carry-on luggage is packed away in the overhead compartments, all purses and such underneath the seat in front of you, your seatbelts on properly, your seats locked in upright positions (seriously, just like the movies!). And then, depending on the airline, you usually get pretzels or peanuts and a drink during the flight.





The landings are what typically make people nervous, atleast the people I've talked to. It's one of my favorite parts though. The pilot will announce they're about to descend, so you know to expect it. If you look out the window, you'll see the ground get closer. They might tip the plane one way or the other in order to turn to the runway. The ground gets closer... but unlike the warning on mirrors "Objects Closer Than They Appear".... really the ground is still further away than you think! You might feel like you're about to run into a tree or something, but I promise, you aren't. The wheels will touch ground, and it may feel like you bounce into the air again. Once the wheels are on the ground, they put on the breaks, and you'll really feel yourself slowing down suddenly. Then they'll taxi around and let you off back into the terminal.





A few tips for your first time flying:





Take gum! Chew it during takeoff and landing. It'll help your ears from popping so badly. I've never had too much problem, but some people do.





Don't carry much with you. You probably won't use half of it, and it makes it easier to get on and off. (And come through security, for that matter.) I usually take a book and a jacket and an I-pod, although some planes have Sirius radio built into the armrests and supply you with headphones. Some people like to carry a change of clothes with them incase their luggage gets lost, but unless you have a lot of layovers I wouldn't worry about it. I've never had them lose my luggage, and lots of times when they DO lose luggage, they end up sending it to you by taxi.





Wear slip on shoes. Really, that's more for security reasons. Lots of airports require you to take your shoes off anyways, so the easier you can make it on yourself, the better.





And lastly.... this is really important.... ENJOY YOURSELF! Some people don't like flying, or do it so much it's nothing special, but it's really one of my favorite things in the world. It never gets old. Like I said, seeing the world drop away like that... it's just amazing. I have a photograph I took over the wing... you can see to the end of the world, really! The horizon line is way off in the distance, you can actually see the curve of Earth. And the sky is such a clear dark blue. Absolutely Stunning. That was just a little sumthin...














NOW TO THE QUESTION U ASKED:





I listen to some music from a C.d. player, Ipod, Mp3 players .. etc. This way, you'll be concentrating on your favorite songs and lip synching it versus thinking about the flight itself. Ok. So peeoples ears pop all the time! I suggest buying gum at the termanol, that way u cant forget or lose it. All u have to do is chew gum when u get on, and went u land. That is the pressure point...GoOd LuCk!!!Since it's your first time you will probably have butterflies in your stomache the whole time, I did. But it's really fine, all that happens is you feel a bit of pressure going up and it's a bit noisy but it will quiet down when you are in the air and if you feel turbulence during your flight don't freak out okay this happens. You can watch t.v. or listen to music during your flight and you get free snacks and drinks!!!! It's great, but the bathrooms are very small which is very uncomfortable so you should use the bathroom at the airport before you get on your plane, if you are a very motion sick person then you should have a barf bag ready and take some pills at the beginning of the flight! When you are landing you feel pressure and a bit of pain in your ears, afterward you will feel like your ears are clogged but that will go away in at least a day!!!! Don't stress about it, just enjoy your flight!!!!





Once you land and the doors open make sure you have all of your stuff, you then leave the plane and go to baggage claim, look for your flight number on the screen on top of one of the conveyor belts and that is where you will find your luggage!!!!You can bring any snack, but liquids, even toothpaste, water, deoderant..must be in a container 3oz or less...say if u have purfume in a 15oz container, and u only have 3oz left, u still cant bring it. Also, u have to bring all your liquids in a quart-sized ziplock bag, FOR CARRY ON ONLY! All other luggage can have any amount of liqid. Sure, u can bring ur psp, gum...i even bring pencils and paper to read etc...With electronics, wait til the captain says to use them.








For clothes, bring lots of shorts and ts...sunblock...beach towels...bathing suit...etc





have a fun and safe trip! here, i asked this question u might find usefull: http://answers.yahoo.com/question/index;鈥?/a>





also visit tsa.gov!! http://www.tsa.gov/|||Carry on your reading materials, pills, cell phones, a pair of shorts, and a pair of sandels. All liquids go in the bags you will check. That means you will NOT carry on your bottled water, lunch, toilet kits, make up bottles, shampoos or sun tan lotions! All that goes in your checked bags. Before handing over your checked bags, look thru your carry-ons again! Pull out anything liquid and throw it in the bags being checked. Once you are thru security you can purchase bottled waters and food to carry on.





Security confiscates any food or water you have. They will also relieve you of any lotion such as hand cream. This is call the Bush Airport Tax Program. Security takes it from you and you then purchase it again after arrival at your vacation destination.





As for the kids, take some form of workbook or little handheld game. Something they can handle on their own. Also, airplanes can be hot and they can be cold. Multi-layer clothing is good b/c they can put on a hoody or strip down to a tee-shirt. Believe me, it's true. Flips are good because they are easy to take off going thru security lines and they will need them in Florida.|||No liquids thats for sure, they will confiscate, unless its under an ounce each i think and in a zip lock plastic baggie.


Another idea is to bring some nibble snacks like granola bars and a set of clothing in case your suitcases decide to go on a different vacation.|||what ever u need on the plane for that trip. just don't bring any liquid on that carry on chk w/ Ur carrier whats not allowed|||If you are looking for a great place to get travel sized items to save space in your carry-on, check out http://www.AllTravelSizes.com