Question

How do you find two unit vectors perpendicular to the xy plane with equation 3x-4y=17?

Answer 1

See below

Explanation:

The x-y plane has 2 natural basis vectors `hat x = ((1),(0),(0))` and `hat y = ((0),(1),(0))`, and orthonormal vector `hat z = ((0),(0),(1))`.

Any ordered pair that satisfies `3x - 4y = 17` is a point that lies on the xy plane. Any vector that connects any 2 such points also lies on that xy plane.

I am afraid that the question does not make much sense to me :(