Question

Find the TRUE statement of the algebraic operations of scalar and vector quantities.

• A. Adding two scalars of different dimensions is possible
• B. Adding a scalar to a vector of the same dimension is possible
• C. Multiplying any two scalars is possible
• D. Multiplying any vector by any scalar is not possible
• E. Adding any two vectors is not possible

Hint:

In algebraic operations, scalars are numbers and can always be multiplied together. Vectors, however, require specific conditions such as the same dimensions for addition or multiplication by scalars.

Answer 1

The Correct Option is C

Option A: Adding two scalars of different dimensions is not possible. Scalars must have the same dimension in order to be added.

Option B: Adding a scalar to a vector of the same dimension is not possible. Scalars and vectors belong to different categories and cannot be directly added.

Option C: Multiplying any two scalars is indeed possible. Scalars are real numbers, and their multiplication follows normal arithmetic rules.

Option D: Multiplying any vector by any scalar is possible. This operation is called scalar multiplication and is a valid operation in vector algebra.

Option E: Adding any two vectors is possible, as long as they are of the same dimension. The addition of vectors is a standard operation in vector algebra.

Step 1: Verifying the Correctness

The multiplication of two scalars, as described in Option C, is always possible since scalars are just numbers, and their multiplication follows the regular arithmetic rules.

Thus, the TRUE statement is:

\[ \boxed{(C) \text{ Multiplying any two scalars is possible.}} \]