Question

Which of the following algebraic operations with scalar and vector physical quantities are meaningful.

(i) adding any two vectors
(ii) adding a scalar to a vector of the same dimensions
(iii) multiplying any vector by any scalar
(iv) multiplying any two scalars
(v) adding any two scalars
(vi) adding a component of a vector to the same vector.

• A. Only (iii) & (iv) are permissible
• B. Only (ii) & (iv) are permissible
  
• C. Only (iii) & (v) are permissible
  
• D. Only (i) (iii) (iv) (v)& (vi) are permissible
  

Answer 1

The correct option is D Only (i) (iii) (iv) (v)& (vi) are permissible

By basic definitions of scale & vector quantities,

(i) we can add two vectors

(ii) adding a scalar and vector is not possible. We can only either add scalar and scalar or vector and vector.

(iii) we can multiply a scalar with a vector this will change only its magnitude.

(iv) multiplication of two scalars is allowed as this is like multiplying two numbers.

(v) addition of two scalars is allowed and is like adding 2 numbers.

(iv) a component of vector is also a vector quantity, so we can add a vector with its component.

so (i) , (iii) , (iv) , (v), (vi) are correct.