If a particle moves from point $P (2,3,5)$ to point $Q (3,4,5)$. Its displacement vector be

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

Given $a+b+c+d=0,$ which of the following statements eare 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 ?

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

A body moves due East with velocity $20\, km/hour$ and then due North with velocity $15 \,km/hour$. The resultant velocity..........$km/hour$