If $ABCDEF$ is a regular hexagon and $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF} = \lambda \overrightarrow{AD}$,then $\lambda = $

If a point $C$ divides the line segment joining the points with the position vectors $2 \hat{i}-3 \hat{j}+2 \hat{k}$ and $3 \hat{i}-\hat{j}-2 \hat{k}$ in the ratio $2: 3$,then the distance of $C$ from the point with position vector $2 \hat{i}-\hat{j}+\hat{k}$ is

If the position vectors of two points $A$ and $B$ are $\vec{a} - 3\vec{b}$ and $6\vec{b} - 2\vec{a}$ respectively,then the position vector of the point dividing $AB$ in the ratio $1 : 2$ is:

$A$ force is a

$A$ vector which is in the direction of $(3, 6, 2)$ and has magnitude $4$ is $.......$

Let $ABC$ be a triangle and $\bar{a}, \bar{b}, \bar{c}$ be the position vectors of $A, B, C$ respectively. If $D$ divides $BC$ in the ratio $2:3$ internally and $E$ divides $CA$ in the ratio $2:1$ internally,then the position vector of the point $P$ which divides $DE$ in the ratio $3:5$ internally is