If $D, E, F$ are respectively the midpoints of $AB, AC$ and $BC$ in $\Delta ABC$,then $\overrightarrow{BE} + \overrightarrow{AF} = $

The vector $\frac{1}{3} (2\hat{i} - 2\hat{j} + \hat{k})$ is ....

If $A(2 \hat{i} + \hat{j} - \hat{k})$, $B(\lambda \hat{i} + 5 \hat{j} + 4 \hat{k})$, $C(-4 \hat{i} + 3 \hat{j} + 2 \hat{k})$ and $D(-\hat{i} - 2 \hat{j} + 3 \hat{k})$ are four points in space such that $\overrightarrow{AB} = x \overrightarrow{AC} + y \overrightarrow{AD}$ for some real numbers $x \neq 0, y \neq 0$, then $17(\lambda + 9) =$ ?

If $\bar{x}$ is a non-zero vector and $k > 0, k \neq 1$,then $\frac{-k \bar{x}}{|\bar{x}|}$ is $.......$ .

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

The zero vector $(0,0,0)$ $........$