Expert: David Hemmer - 6/6/2007

Question
I was wondering if you could please tell me hoe to change point normal form of a vector into vector parametric form. this is the question I have:

Find the equations of the following planes in both cartesian and (vector) parametric form:
The plane through the point (1, 4, 5) and perpendicular to the vector (7, 1, 4).

Answer
Vector form:

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

the * is a dot product. This is just saying that for any point (x,y,z) on the plane, the vector (x-1,y-4,z-5) must be in the plane and thus perpendicular to (7,1,4).

The cartestion form is going to be of the form 7x+y+4z=d, to get d just plug in the point (1,4,5) and you will see that d is 31.