When vector $\overrightarrow{A} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ is subtracted from vector $\vec{B}$,it gives a vector equal to $2\hat{j}$. Then the magnitude of vector $\vec{B}$ will be:

The direction cosines of vector $(A - B)$,if $A = 2\hat{i} + 3\hat{j} + \hat{k}$ and $B = 2\hat{i} + 2\hat{j} + 3\hat{k}$,are:

The figure shows three vectors $p$,$q$,and $r$,where $C$ is the midpoint of $AB$. Which of the following relations is correct?

Is it possible that $\vec{A} + \vec{B} = \vec{A} - \vec{B}$?

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis,respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$,respectively. The magnitude of the resultant vector of these two vectors is ....... $m$.

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces