Question

If $||u\times v||=||u||||v||$, what is the geometric relationship between u and v?

Short answer

The vectors u and v are orthogonal.

Step-by-step solution

Step 1. Given Information 

If $||u\times v||=||u||||v||$, what is the geometric relationship between u and v?

Step 2. As we know u×v=uvsinθ

If $||u\times v||=||u||||v||$then

$$\begin{gathered} \sin \theta =1 \\ \theta ={90}^o \end{gathered}$$

Then the relation between u and v, $u\times v$is perpendicular to any plane containing both u and v.

The vectors u and v are orthogonal.