Question

$ \hat{u} $ and $ \hat{v} $ are unit vectors such that $ \hat{u}\,\,.\hat{v} = 0 $ . If $ \vec{r} $ is any vector coplanar with $ \vec{u} $ and $ \vec{v} $ then the magnitude of the vector $\vec{r} \times (\hat{u} \times \hat{v})$ is :

• A. $ 0 $
• B. $ 1 $
• C. $ |\vec{r}| $
• D. $ 2|\vec{r}| $

Answer 1

Answer: (C)

Given, $ |\vec{u}|=|\vec{v}|=1 $
and $ \vec{u}\,.\,\vec{v}=0 $
ie, angle between
$ \vec{u} $ and $ \vec{v} $ is $ {{90}^{o}} $
$ \therefore $ $ |\vec{u}\times \vec{v}| =|\vec{u}||\vec{v}|\,\sin \theta =1 $