Browse Questions

# If $\overrightarrow u=\hat i+\hat j,\:\overrightarrow v=\hat i-\hat j\:\:and\:\:\overrightarrow w=\hat i+2\hat j+3\hat k$. and if $\hat n$ is a unit vector such that $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$, then $|\overrightarrow w.\hat n|=?$

Let $\hat n=x\hat i+y\hat j+z\hat k$
Given: $\overrightarrow u.\hat n=\overrightarrow v.\hat n=0$
$\Rightarrow\:x+y=0\:\:and\:\:x-y=0$
$\Rightarrow\:x=y=0$
since $\hat n$ is a unit vector, $z=\pm 1$
$\therefore\:|\overrightarrow w.\hat n|=|x+2y+3z|=3$