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# 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.

Last updated date: 23rd Jun 2024
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Hint: To determine whether these operations are meaningful, consider the fundamental properties of scalar and vector quantities and how these operations relate to those properties.

Step-by-Step Solutions:

• Explanation: Adding two scalars is meaningful because scalars have only magnitude and no direction. You can simply add their numerical values.

(b) Adding a scalar to a vector of the same dimensions:

• Explanation: This is meaningful because it's equivalent to scaling the vector by the scalar quantity. For example, if you add a scalar speed to a vector velocity, you are just changing the magnitude of the vector in the same direction.

(c) Multiplying any vector by any scalar:

• Explanation: Multiplying a vector by a scalar is meaningful and represents a scaling or stretching of the vector. The direction of the vector remains the same, but its magnitude is scaled by the scalar.

(d) Multiplying any two scalars:

• Explanation: Multiplying two scalars is also meaningful. This operation results in another scalar, representing the product of the two numerical values. It is a fundamental mathematical operation.