$A$ vector of magnitude $14$ lies in the $xy-$ plane and makes an angle of $60^\circ$ with the $x-$ axis. The components of the vector in the direction of the $x-$ axis and $y-$ axis are:

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

If two vertices of a triangle are $\hat{i} - \hat{j}$ and $\hat{j} + \hat{k}$,then the third vertex can be

If $P \hat{i}-2 \hat{j}+3 \hat{k}$, $2 \hat{i}+3 \hat{j}-4 \hat{k}$, and $4 \hat{i}+13 \hat{j}-18 \hat{k}$ are the position vectors of three collinear points $A$, $B$, and $C$ respectively, then the vector in the direction of $AB$ of length $|P|$ units is

Write down a unit vector in the $XY$-plane,making an angle of $30^{\circ}$ with the positive direction of the $x$-axis.

The points having position vectors $2i + 3j + 4k,$ $3i + 4j + 2k,$ and $4i + 2j + 3k$ are the vertices of: