If $$\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$$ and $$\mathbf{r}=\hat{i}+\hat{k}$$, then the unit vector in the direction of $$3 p+q-2 r$$ is

The vector that must be added to $$\widehat i - 3\widehat j + 2\widehat k$$ and $$3\widehat i + 6\widehat j - 7\widehat k$$ so resultant vector is a unit vector along the X-axis is

If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b.

If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i + \widehat j + 2\widehat k$$, then find $$[a\,b\,c]$$.