Question

Which of the following operations makes no sense in case of scalars and vectors:
A. Multiplying any vector by a scalar
B. Adding a component of a vector to the same vector
C. Multiplying any two scalars
D. Adding a scalar to a vector of the same dimension

Answer 1

Hint: This question requires the knowledge of the basics of scalars and vectors. Scalars are the quantities that have only magnitude and do not represent any direction. Vector quantities have both magnitude as well as direction. So, the arithmetic properties that are applied on these quantities are different.

Complete step-by-step solution:
Simple arithmetic rules do not apply to the addition and subtraction of vector numbers. The addition and subtraction of vectors are done according to a set of rules. The arithmetic operations that can be carried between scalars and vectors are limited:
A vector quantity can be multiplied or divided by a scalar quantity where each vector component should be divided by the scalar quantity.
Addition of vector components to the same vector or even a different vector is possible. It follows the laws of vector addition.
The multiplication of any number of scalar quantities is carried out in the same way as basic multiplication is done.
However, we cannot directly add a scalar quantity to a vector quantity. This is against the laws of vector addition. So, the correct answer for the above question (d).

Note: Finding the outcome of a number of vectors acting on a body is known as vector addition. The component vectors that make up the outcome are unrelated to one another. Each vector behaves as though the others aren't there. Geometrically, but not algebraically, vectors can be added.