Establish the following vector inequalities geometrically or otherwise :

$|a+b|\le \left|a\right|+\left|b\right|$

$|a+b|\ge \left|a\right|-\left|b\right|$

$|a-b|\le \left|a\right|+\left|b\right|$

$|a-b|\ge \left|a\right|-\left|b\right|$

The magnitude of a vector is always a scalar.

Each component of a vector is always a scalar.

Three vectors not lying in a plane can never add up to give a null vector.

State with reason, whether the following algebraic operation with scalar and vector physical quantities are meaningful:

adding any two scalars.