$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Find $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \ldots \ldots$.

What is the minimum number of non-zero vectors in different planes that can be added to give a zero resultant?

The vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ lie in a plane. Another vector $\overrightarrow{C}$ lies outside this plane. The resultant $\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ of these three vectors:

If a unit vector is represented as $\overrightarrow{u} = 0.4 \hat{i} + 0.7 \hat{j} + c \hat{k}$,then the value of '$c$' is

$A$ man goes $10\,m$ towards North,then $20\,m$ towards East. The displacement is ........ $m$.

What is a position vector? What is a displacement vector? Explain the equality of vectors.