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

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following  vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$     $(B)$ $\hat a + \widehat b$     $(C)$ $\hat a$      $(D)$ $\hat b$

Which of the following forces cannot be a resultant of $5\, N$ and $7\, N$ force...........$N$

If the sum of two unit vectors is a unit vector, then magnitude of difference is

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 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