More old material planes, normal and parallel vectors

[1MileCrash]

Homework Statement

Consider z = -3x - y + 11

Find a unit vector perpendicular to the plane, and find a vector parallel to the plane.

Homework Equations

The Attempt at a Solution

1.)

0 = -3x - y + 11 - z
-11 = - 3x - y - z

Perpendicular vector is then:

-3i -j -k

And to make that a unit vector, divide it by sqrt(11)


2.)

Here's what I'm not sure of. Can I just pick anything that gives me a dot product of 0 with the above?

Such that:

- 3a - b - c = 0?

Choosing a = -3, b = 5, c = 4,

A parallel vector to the plane is -3i + 5j + 4k?

Or is that incorrect?

 

[LCKurtz]

It is all correct.

 

[1MileCrash]

Thank you sir.