Let u= i+ j, v= i- j and w= i+2 j+3 k.

Question

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 $\vec u\cdot\hat n=0$ and $\vec v\cdot\hat n=0$, then $\vec w\cdot\hat n$ is equal to:

Accepted Answer

$\hat n$ is parallel to $\vec u\times\vec v = \begin{vmatrix}\hat i&\hat j&\hat k\1&1&0\1&-1&0\end{vmatrix}=-2\hat k$, so $\hat n=\pm\hat k$.

$$\vec w\cdot\hat n = |(\hat i+2\hat j+3\hat k)\cdot(\pm\hat k)| = 3$$

Solutions · 1