Plane Equations with Vector and Parametric Forms | Homework Solution"

[Buzzlastyear]

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

The Attempt at a Solution

I think my answer is correct but it seems to simple to be right:

Just sub in a(2,3,-1) into (x, y, z) = (2, 1, -3) + s(5, 2, -1) + t(3, -2, 4) as the point.

so:

(x,y,z)=(2,3,-1) + s(5,2,-1) + t(3,-2,4)
(x,y,z)=(2+5s+3t, 3+2s-2t, -1-s+4t)
x=2+5s+3t
y=3+2s-2t
z=-1-s+4t

Any help is appreciated thank you

 

[tiny-tim]

Hi Buzzlastyear!

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).
…
(x,y,z)=(2+5s+3t, 3+2s-2t, -1-s+4t)

Yes, that's fine for the parametric equation.

You still need the vector equation (with dot or cross product). ​

 

[Buzzlastyear]

Thank you!