Question

Assertion: Multiplying any vector by a scalar is a meaningful operation.
Reason: In uniform motion speed remains constant.
A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
C. Assertion is true but reason is false.
D. Both assertion and reason are false.

Answer 1

Hint: In this question we will use the concept of scalars and vectors and the arithmetic rules to multiply a scalar and a vector.

Complete step by step solution:
The given assertion is that multiplying any vector by a scalar is a meaningful operation. This statement is correct since scalar is a magnitude, if we multiply it with a quantity having magnitude as well as direction, that is a vector quantity, a new vector quantity with higher magnitude will be formed. For example, when mass, a scalar quantity is multiplied with acceleration, a vector quantity, we get force, another vector quantity.

The given reason statement is that in uniform motion speed remains constant. This statement is also correct since when an object moves uniformly, it travels in a straight line with a constant speed along that path, covering equal distances in similar amounts of time, regardless of how long the time intervals last. But the reason statement is not the correct explanation of the assertion statement. Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Hence, the correct answer is B.

Note: A vector's size gets "scaled" up or down when it is multiplied by a scalar. A vector's magnitude, not its direction, will change when it is multiplied by a positive scalar. A negative scalar will cause a vector's direction to be reversed when multiplied by it. The addition and subtraction of vectors are conducted according to a unique set of guidelines. Finding the product of several vectors acting on a body is known as adding vectors.