If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then .....

If the vectors represented by the sides $AB$ and $BC$ of the regular hexagon $ABCDEF$ are $a$ and $b$ respectively,then the vector represented by $\overrightarrow{AE}$ will be

If $a, b, c$ are three non-coplanar vectors such that $a + b + c = \alpha d$ and $b + c + d = \beta a$,then $a + b + c + d$ is equal to

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}$,$\bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$,then the unit vector in the direction of $3 \bar{a}+\bar{b}-2 \bar{c}$ is

The vectors $3i + j - 5k$ and $ai + bj - 15k$ are collinear if $....$

If $\vec{a}$ and $\vec{b}$ are the position vectors $(P.V.)$ of two points $A$ and $B$ respectively,and $C$ divides the line segment $AB$ in the ratio $2 : 1$,then the position vector of $C$ is: