Question

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

1. adding any two scalars, 

2. adding a scalar to a vector of the same dimensions, 

3. multiplying any vector by any scalar, 

4. multiplying any two scalars, 

5. adding any two vectors, 

6. adding a component of a vector to the same vector.

Answer 1

1. Not meaningful. Two scalars of different dimensions/units cannot be added. 

2. Not meaningful. A scalar and a vector cannot be added. 

3. Meaningful. A scalar and vector can be multiplied irrespective of their dimensions/units. 

4. Meaningful. Two scalars can be multiplied irrespective of their dimensions/units. 

5. Not meaningful. Two vectors of different dimensions/units cannot be added. 

6. Not meaningful. A component of a vector cannot be added to it.