Finding vectors parallel and perpendicular to plane

[1MileCrash]

Homework Statement

Find a vector perpendicular to plane z = 5 + 3x - y, and find a vector parallel to the plane.

Homework Equations

The Attempt at a Solution

The normal vector is simple, because my book addresses it. It is 3i - j - k.

I have absolutely no clue how to get a parallel vector to the plane. Any hints?

 

[Froster78]

I've been thinking about this one for a bit. If you had another vector perp to the plane you could use a cross product. Also, you might have more luck on the calculus page.

 

[1MileCrash]

I've been getting really frustrated over this one. My only way of solving is that I know that the parallel vector is perpendicular to the normal vector, so therefore the dot product of those two vectors is 0, but that gives me infinite possibilities for the parallel vector... and there is a specific one the homework wants. Makes no sense to me at all.

 

[Froster78]

A cross product of two vectors perpendicular to the plane will give you a vector parallel to the plane.

 

[1MileCrash]

A cross product of two vectors perpendicular to the plane will give you a vector parallel to the plane.

And where do I get this second perpendicular vector?

 

[Froster78]

Ok, I think I have a better idea... Sorry I'm really using this to help myself as well. If you find two points, say (0,0,0) and (1,1,1) just using arbitrary points on your plane. You can construct a vector using the initial and terminal points. This vector should be parallel to the plane. You could obviously check this by the dot product with the normal vector.

does that help?