While travelling from one station to another,a car travels $75 \, km$ North,$60 \, km$ North-east,and $20 \, km$ East. The minimum distance between the two stations is.......$km$

If the magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector,then find the angle between the two vectors. (in $^{\circ}$)

The vector that must be added to the vectors $\hat{i} - 3\hat{j} + 2\hat{k}$ and $3\hat{i} + 6\hat{j} - 7\hat{k}$ so that the resultant vector is a unit vector along the $y$-axis is

Match List-$I$ with List-$II$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then the magnitude of $\vec{C}$ is

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)