Question

If u and v are vectors in ${\mathrm{ℝ}}^3$ such that $u\times v=v\times u$, what can we conclude about u and v?

Short answer

We conclude about u and v that they are parallel.

Step-by-step solution

Step 1. Given Information 

If u and v are vectors in${\mathrm{ℝ}}^3$such that $u\times v=v\times u$, what can we conclude about u andv?

Step 2. We conclude about u and v:

The cross product may be the first product you’ve encountered that is not commutative. However, it is anti-commutative. That is, for every two vectors u and v in ${\mathrm{ℝ}}^3$, we have the following:

$v\times u=u\times v$

We conclude about u and vthat they are parallel.