The scalar components of a unit vector which is perpendicular to each of the vectors $$\hat{\imath}+2 \hat{\jmath}-\hat{k}$$ and $$3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$$ are

$$ \text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is } $$

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