Let \(\mathbf{u}\) and \(\mathbf{v}\) be two non-zero vectors. Then the magnitude of the cross product…
Let \(\mathbf{u}\) and \(\mathbf{v}\) be two non-zero vectors. Then the magnitude of the cross product \(\mathbf{u} \times \mathbf{v}\) is always
\( < |u||v|\)
\(=|u||v|\)
\(>|u||v|\)
\(=0\)
Solution
The cross product of \(u\) and \(v\) non-zero vectors is \(\mathbf{u} \times \mathbf{v}=|\mathbf{u} \| \mathbf{v}| \sin \theta \hat{\mathbf{n}}\), if angle between them is \(\theta\).
So, \(\quad|u \times v|=|u||v||\sin \theta|\)
\(\Rightarrow \quad|u \times v| \leq|u||v| \quad \therefore|\sin \theta| \leq 1\)