$100$ coplanar forces each equal to $10 \,N$ act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$

Establish the following vector inequalities geometrically or otherwise:

$(a)$ $\quad| a + b | \leq| a |+| b |$

$(b)$ $\quad| a + b | \geq| a |-| b |$

$(c)$ $\quad| a - b | \leq| a |+| b |$

$(d)$ $\quad| a - b | \geq| a |-| b |$

When does the equality sign above apply?

The maximum and minimum magnitude of the resultant of two given vectors are $17 $ units and $7$ unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

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

Two forces, each of magnitude $F$ have a resultant of the same magnitude $F$. The angle between the two forces is....... $^o$

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C= 0$ out of three vectors two are equal in magnitude and the magnitude of third vector is $\sqrt 2 $ times that of either of the two having equal magnitude. Then the angles between vectors are given by