Establish the following vector inequalities geometrically or otherwise :

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

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.

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

adding a scalar to a vector of the same dimensions.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

multiplying any vector by any scalar.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

multiplying any two scalars.