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

1 Answer
Feb 24, 2017

See below


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 :(