How Do You Formulate a Vector Equation for a Plane Given Points and Directions?

[DespicableMe]

Homework Statement

Write a vector and parametric equation for a plane that:

b) contains (-5,9,-3) and is parallel to [x,y,z] = [1, -2, 7] + s[4, -1, -3] and

[x,y,z] = [7,-2,15] + t[1,6,-8]

The Attempt at a Solution

I'm not sure where to start. Usually, when asking for parallel lines, I find if the direction vectors are scalar multiples of each other, then I find out if s and t have the same value for all x y and z.



I'm confused about planes.
What they had as the answer was the exact same direction vectors s and t, and then the point given as r nought.

 

[HallsofIvy]

The vector form for a plane is
$$\vec{r}= (x_0+ As+ Bt)\vec{i}+ (y_0+ Cs+ Dt)\vec{j}+ (z_0+ Es+ Ft)\vec{k}$$
where $(x_0, y_0, z_0)$ is any point in the plane and
$$A\vec{i}+ C\vec{j}+ E\vec{k}$$
and
$$B\vec{i}+ D\vec{j}+ F\vex{k}$$
are two vectors in the plane.

In your question, you are given all three of those things.