Find two unit vectors orthogonal to <2,2,4>. Can you find others?

Answer 1

There are an infinite number of such vectors. An orthogonal vector is one whose dot product with the given vector is zero. To make it a unit vector, divide it by its magnitude.

Example 1: u = (1/√3)<1, 1, -1>

u • <2, 2, 4> = (1/√3)<1, 1, -1> • <2, 2, 4>
= (2 + 2 - 4)/√3 = 0

Example 2: v = (1/√5)<2, 0, -1>

v • <2, 2, 4> = (1/√5)<2, 0, -1> • <2, 2, 4>
= (4 + 0 - 4)/√5 = 0