Q. 11 - Calculus

Question

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

Step-by-Step Solution

Answer

The vectors u and v are orthogonal.

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 = u v sin θ

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.