$A, B, C, D, E$ are five coplanar points,then $\overrightarrow{DA} + \overrightarrow{DB} + \overrightarrow{DC} + \overrightarrow{AE} + \overrightarrow{BE} + \overrightarrow{CE}$ is equal to

Let $A(3 \hat{i}+\hat{j}-\hat{k})$ and $B(13 \hat{i}-4 \hat{j}+9 \hat{k})$ be two points on a line $L$. $C$ and $D$ are points on $L$ on either side of $A$ at distances of $9$ and $6$ units respectively,and $C$ lies between $A$ and $B$. Then the position vectors of $C$ and $D$ are respectively:

Write two different vectors having the same direction.

If the vectors $2 \hat{i}-3 \hat{j}+6 \hat{k}$ and $\vec{b}$ are collinear and $|\vec{b}|=14$,then $\vec{b}$ has the value

If $\hat{x}, \hat{y},$ and $\hat{z}$ are three unit vectors in three-dimensional space,then find the minimum value of $|\hat{x} + \hat{y}|^2 + |\hat{y} + \hat{z}|^2 + |\hat{z} + \hat{x}|^2$.

If $\vec{a}, \vec{b}, \vec{c}, \vec{d}$ are position vectors of $4$ points such that $2 \vec{a}+3 \vec{b}+5 \vec{c}-10 \vec{d}=\vec{0}$,then the ratio in which the line joining $\vec{c}$ and $\vec{d}$ divides the line segment joining $\vec{a}$ and $\vec{b}$ is