A unit vector perpendicular to both $\hat i +\hat j$ and $\hat j+\hat k$, is |
$\hat i-\hat j+\hat k$ $\hat i+\hat j+\hat k$ $\frac{\hat i+\hat j+\hat k}{\sqrt{3}}$ $\frac{\hat i-\hat j+\hat k}{\sqrt{3}}$ |
$\frac{\hat i+\hat j+\hat k}{\sqrt{3}}$ |
Let $\vec a=\hat i +\hat j$ and $\vec b=\hat j+\hat k$. Then, $\vec a×\vec b=\begin{vmatrix}\hat i&\hat j&\hat k\\1&1&0\\0&1&1\end{vmatrix}=\hat i-\hat j+\hat k$ ∴ Required vectors = $±\frac{\hat i-\hat j+\hat k}{\sqrt{1^2+(-1)^2+1^2}}=±\frac{\hat i+\hat j+\hat k}{\sqrt{3}}$ |