__Question 4.4__:

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

(a) adding any two scalars,

(b) adding a scalar to a vector of the same dimensions,

(c) multiplying any vector by any scalar,

(d) multiplying any two scalars,

(e) adding any two vectors,

(f) adding a component of a vector to the same vector.

__Solution__:

**Answer:**

(a) Meaningful

(b) Not Meaningful

(c) Meaningful

(d) Meaningful

(e) Meaningful

(f) Meaningful

**Explanation:**

**(a)**The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.

**(b)**The addition of a vector quantity with a scalar quantity is not meaningful.

**(c)**A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.

**(d)**A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.

**(e)**The addition of two vector quantities is meaningful only if they both represent the same physical quantity.

**(f)**A component of a vector can be added to the same vector as they both have the same dimensions.

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