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
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 and Explanation
a) adding any two scalars - Meaningful
Explanation: The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
(b) adding a scalar to a vector of the same dimensions - Not Meaningful
Explanation: The addition of a vector quantity with a scalar quantity is not meaningful.
(c) multiplying any vector by any scalar - Meaningful
Explanation: A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
(d) multiplying any two scalars - Meaningful
Explanation: A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
(e) adding any two vectors - Meaningful
Explanation: The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
(f) adding a component of a vector to the same vector - Meaningful
Explanation: A component of a vector can be added to the same vector as they both have the same dimensions.
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