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

The components of a vector $\vec{a}$ with respect to a rectangular Cartesian system are $2p$ and $1$. The system is rotated about the origin through a certain angle in the counter-clockwise direction. If the components of $\vec{a}$ with respect to the new system are $p + 1$ and $1$,then:

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a}_1=2 \hat{i}-\hat{j}+\hat{k}$, $\overrightarrow{a}_2=3 \hat{i}-4 \hat{j}-4 \hat{k}$, $\overrightarrow{a}_3=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{a}_4=-\hat{i}+3 \hat{j}+\hat{k}$, then the correct order of $m_1, m_2, m_3$ and $m_4$ is

Find the unit vector in the direction of vector $\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}$.

In a parallelogram $ABCD$,if the diagonals are $\overline{AC}$ and $\overline{BD}$,then $\overline{AC} - \overline{BD} = \dots$

If $\vec{a} \cdot \vec{a}=0$ and $\vec{a} \cdot \vec{b}=0,$ then what can be concluded about the vector $\vec{b}$?