Question

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

Answer 1

a) adding any two scalars - Meaningful

Explanation: The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.

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** (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.

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(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.

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**(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.

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**(e) adding any two vectors - **Meaningful

**Explanation: **The addition of two vector quantities is meaningful only if they both represent the same physical quantity.

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** (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.