Thread: Vector equation of a plane

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]

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.

Originally Posted by TN17

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]

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.

One way to find the equation of a plane is to know a normal vector to the plane and a point in the plane. Since we have the point we need to find a normal vector to the plane. Since the plane must be parallel to both of the above lines we can find a vector perpendicular to both of them by taking the cross product of the direction vectors.



Can you finish from here?