Let $\vec u=\hat i+\hat j, \vec v=\hat i-\hat j$ and $\vec w=\hat i+2\hat j+3\hat k$. If $\hat n$ is a unit vector such that $\vec u.\hat n=0$ and $\vec v.\hat n=0$, then $|\vec w.\hat n|$ is equal to
Answer & explanation
Correct answer: option 1
We have,
$\vec u.\hat n=0$ and $\vec v.\hat n=0$
$∴\hat n⊥\vec u$ and $\hat n⊥\vec v$$⇒\hat n=±\frac{\vec u×\vec v}{|\vec u×\vec v|}$
Now, $\vec u×\vec v=(\hat i+\hat j)×(\hat i-\hat j)=-2\hat k$
$∴\hat n=±\hat k$
Hence, $|\vec w.\hat n|=|(\hat i+2\hat j+3\hat k).(±\hat k)|=3$