- #1

rafehi

- 49

- 1

## Homework Statement

Find the equation of the following planes in cartesian and (vector) parametric form:

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

b) the plane through the origin and the points (1,1,1) and (1,2,3)

## The Attempt at a Solution

For part a)

I found the cartesian form of the equation using a(x-x0) + b(y-y0) + c(z-z0), to give:

7(x-1) + 1(y-4) + 4(z-5) = 0, which expands to:

7x + y + 4z = 31, which is correct.

However, I've no idea how to find the parametric form. The answer is given as r = (1,4,5) + s(4,0,-7) + t(0,4-1).

Any help on how I'd go about answering this question?

For part b)

To find the cartesian form, I found the vectors from the origin to (1, 1, 1,) and (1, 2, 3), using V1->V2 = V2 - V1, giving me V0->V1= (1,1,1) and V0->V2 = (1,2,3). Using the cross product to get the orthogonal, then dotting that with (0,0,0) gives the correct equation, x-2y+z=0, which is correct.

Again, I've got no idea how to find the parametric equation.

Any help would be greatly appreciated. These aren't assignment questions or anything like that - just revision for my L.A exam next week.