If $$\theta$$ be the angle between the vectors $$a = 2\widehat i + 2\widehat j - \widehat k$$ and $$b = 6\widehat i - 3\widehat j + 2\widehat k$$, then

If x, y and z are non-zero real numbers and $$a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k$$ and $$c = x\widehat i + y\widehat j + z\widehat k$$ are such that $$a \times b = z\widehat i - 3\widehat j + \widehat k$$, then [a b c] is equal to

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