1. ## Orthogonal Vectors

Let u = <-1, 1, 2> and v = <2, -1, -1>. Find all unit vectors orthogonal to both u and v.

I know that one can use cross products to find a vector orthgonal to both u and v and scale it down to be a unit vector. But the question says to find all the unit vectors and I don't know how to go about doing that since there is an infinite number of them.

2. It is really simple: $\pm \frac{{u \times v}}{{\left\| {u \times v} \right\|}}$.

3. So, the answer would be + or -(i + 3j - k)/(sqrt 11) ? Or would I go ahead and say it's <(1/(sqrt 11)), (3/(sqrt 11)), (-1)/(sqrt11)> But isn't that just one unit vector orthogonal to u and v, not all of them?

4. Originally Posted by kiddopop
But isn't that just one unit vector orthogonal to u and v, not all of them?
What do you think $\pm$ means?