If the resultant of $n$ forces of different magnitudes acting at a point is zero, then the minimum value of $n$ is

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. Find $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=.......$

Two vectors $\dot{A}$ and $\dot{B}$ are defined as $\dot{A}=a \hat{i}$ and $\overrightarrow{\mathrm{B}}=\mathrm{a}(\cos \omega t \hat{\mathrm{i}}+\sin \omega t \hat{j}$ ), where a is a constant and $\omega=\pi / 6 \mathrm{rad} \mathrm{s}^{-1}$. If $|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=\sqrt{3}|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|$ at time $t=\tau$ for the first time, the value of $\tau$, in, seconds, is. . . . . .

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

A particle is simultaneously acted by two forces equal to $4\, N$ and $3 \,N$. The net force on the particle is

Explain subtraction of vectors.