$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is

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