If $D, E$ and $F$ are respectively the mid-points of $AB, AC$ and $BC$ in $\triangle ABC$, then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to :

If $P$ and $Q$ are two points on the curve $y=2^{x+2}$ such that $OP \cdot \hat{i}=-1$ and $OQ \cdot \hat{i}=2$,then the magnitude of $(OQ-4OP)$ is

If $\vec{p} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{q} = \hat{i} + \hat{j} - \hat{k}$,and $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{p} = 2\vec{a} + \vec{b}$ and $\vec{q} = \vec{a} + 2\vec{b}$,then the angle between $\vec{a}$ and $\vec{b}$ is:

The line joining the points $6 \overrightarrow{a}-4 \overrightarrow{b}+4 \overrightarrow{c}$ and $-4 \overrightarrow{c}$ and the line joining the points $-\overrightarrow{a}-2 \overrightarrow{b}-3 \overrightarrow{c}$ and $\overrightarrow{a}+2 \overrightarrow{b}-5 \overrightarrow{c}$ intersect at:

If $|a| = 3, |b| = 4$ and $|a + b| = 5,$ then $|a - b| = $

Classify the following measure as a scalar or a vector:
$10 \text{ kg}$