The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$

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 resultant of $\overrightarrow A + \overrightarrow B $ is ${\overrightarrow R _1}.$ On reversing the vector $\overrightarrow {B,} $ the resultant becomes ${\overrightarrow R _2}.$ What is the value of $R_1^2 + R_2^2$

Two forces $3\,N$ and $2\, N$ are at an angle $\theta$ such that the resultant is $R$. The first force is now increased to $ 6\,N$ and the resultant become $2R$. The value of is ....... $^o$

If $|{\overrightarrow V _1} + {\overrightarrow V _2}|\, = \,|{\overrightarrow V _1} - {\overrightarrow V _2}|$ and ${V_2}$ is finite, then

How many minimum number of non-zero vectors in different planes can be added to give zero resultant