If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel,then $\lambda$ is

If $a = \alpha \hat{i} + 3 \hat{j} - 6 \hat{k}$ and $b = 2 \hat{i} - \hat{j} + \beta \hat{k}$,then the values of $\alpha, \beta$ so that $a$ and $b$ may be collinear are

If $\vec{a} = \hat{i} + \hat{j} - 2 \hat{k}$,$\vec{b} = 2 \hat{i} - \hat{j} + \hat{k}$ and $\vec{c} = 3 \hat{i} - \hat{k}$. If $\vec{c} = m \vec{a} + n \vec{b}$ then $m + n = $

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $|\overrightarrow{a}+\overrightarrow{b}|=1$,then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

If $r \cdot i = r \cdot j = r \cdot k$ and $|r| = 3$, then $r = $

If $ABCDEF$ is a regular hexagon with $\vec{AB} = \vec{a}$ and $\vec{BC} = \vec{b}$,then $\vec{CE}$ equals to