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

$A$ vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects? Give examples in support of your answer.

Find $|\Delta \overrightarrow{a}|$ and $\Delta a$ when a vector $\overrightarrow{a}$ is rotated by an angle $d\theta$.

Given $a+b+c+d=0,$ which of the following statements are correct:
$(a)$ $a, b, c,$ and $d$ must each be a null vector.
$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$.
$(c)$ The magnitude of $a$ can never be greater than the sum of the magnitudes of $b, c,$ and $d$.
$(d)$ $(b+c)$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear,and in the line of $a$ and $d$ if they are collinear.

When a particle moves from point $A(2,2,3)$ to point $B(6,6,9)$,its displacement vector is

Define scalar and vector physical quantities with their examples.