How do you find both vector and Cartesian equation of a plane?

(a) the plane through the point (1,4,5) and perpendicular to the vector (7,1,4)


(b) the plane through the point (6,5-2) and parallel to the plane x + y - z + 1 = 0|||(a)eqation of a plane equals point time normal vector so egation equals


7(x-1)+1(y-4)+4(z-5)=0


7x-7+y-4+4z-20=0


7x+y+4z-31=0





(b)since its parallel then the planes have same vector or multiple of the vector.


1(x-6)+1(y-5)+1(z+2)=0


x-6+y-5+z+2=0


x+y+z-9=0