Plane w/ Point A & Parallel to Plane w/ Equation

[unknown101]

Homework Statement

Determine vector and parametric equations for the plane containing the point A(2, 3, -1) and parallel to the plane with equation (x, y, z) = (2, 1, -3) + s(5, 2, -1) + t(3, -2, 4). Show your work.

Homework Equations

Vector and parametric
This a strange equation that I have never seen before because it has 2 parameters: s and t

The Attempt at a Solution

I got the parametric equation for the x, y,z equation
x=2+5s+3t
y=1+2s-2t
z=-3-t+4t

Am I supposed to find the direction vector? In one of my notes is says that the direction vector is perpendicular to the plane's normal vector but I don't know if it applies here?

 

[tiny-tim]

Determine vector and parametric equations for the plane containing the point A(2, 3, -1) and parallel to the plane with equation (x, y, z) = (2, 1, -3) + s(5, 2, -1) + t(3, -2, 4). Show your work.

Hi unknown101!

I think what they mean by "vector and parametric equations" is that the vector and parametric equation for the original plane is (x, y, z) = (2, 1, -3) + s(5, 2, -1) + t(3, -2, 4)

 

[unknown101]

Hi unknown101!

I think what they mean by "vector and parametric equations" is that the vector and parametric equation for the original plane is (x, y, z) = (2, 1, -3) + s(5, 2, -1) + t(3, -2, 4)

So would the equation for the new equation be (x,y,z)=(2,3,-1)+s(5, 2, -1) + t(3, -2, 4).

 

[tiny-tim]

So would the equation for the new equation be (x,y,z)=(2,3,-1)+s(5, 2, -1) + t(3, -2, 4).

Yup!

 

[unknown101]

Yup!

Thanks a lot:)