What should be the angle $\theta$ between two vectors $\vec{A}$ and $\vec{B}$ so that the magnitude of the resultant vector is minimum (in $^{\circ}$)?

The angle made by the resultant vector of two vectors $2 \hat{i}+3 \hat{j}+4 \hat{k}$ and $2 \hat{i}-7 \hat{j}-4 \hat{k}$ with the $x$-axis is (in $^{\circ}$)

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

If two forces of equal magnitudes act simultaneously on a body in the east and the north directions,then:

$A$ particle moves $21 \ m$ along the direction of the vector $6\hat{i} + 2\hat{j} + 3\hat{k}$,then it moves $14 \ m$ along the direction of the vector $3\hat{i} - 2\hat{j} + 6\hat{k}$. What is its total displacement (in meters)?

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 ....... $m$.