Which of the following is meaningful

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\frac{Vector}{Vector}

\frac{Vector}{Scalar}

Scalar + vector

\frac{Scalar}{Vector}

answer is D.

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Detailed Solution

The question provides several options involving scalar and vector quantities. Let’s analyze each option to determine which of the following is not meaningful:

Option A: Vector / Vector
Division of two vectors is undefined in physics because vectors possess both magnitude and direction, and the operation of division does not preserve directional properties. Hence, this operation is not meaningful.
Option B: Scalar / Vector
Division of a scalar by a vector is not defined because a scalar has no direction, whereas a vector does. Combining the two in a division operation results in a physically meaningless quantity. Thus, this option is not meaningful.
Option C: Scalar + Vector
Adding a scalar to a vector is not possible because a scalar lacks direction while a vector has both magnitude and direction. The two quantities are incompatible for addition, making this operation meaningless. Therefore, this is another example of which of the following is not meaningful.

After careful evaluation, all three options—A, B, and C—are operations that are not meaningful in the context of scalar and vector arithmetic.

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