Final Answer:
Adding a scalar to a vector is not possible as it violates the fundamental properties of vector addition, where both operands must have the same dimensionality. Mathematically, the operation is undefined, and conceptually, it contradicts the nature of vectors and scalars.Thus the correct option is option b.
Step-by-step explanation:
Adding a scalar quantity to a vector quantity is not mathematically feasible. Scalars are quantities that have only magnitude, while vectors have both magnitude and direction. Attempting to add a scalar to a vector implies combining a one-dimensional quantity with a multidimensional one, leading to an incompatible operation.
In mathematical terms, let's consider a vector V = (V₁, V₂, V₃) and a scalar S. The addition of these two would imply V + S = (V₁ + S, V₂ + S, V₃ + S). However, this operation is undefined because it violates the fundamental properties of vector addition. Vector addition demands that both operands possess the same dimensionality, which is not the case when attempting to add a scalar to a vector.
Moreover, the geometric interpretation reinforces the impossibility of this operation. Vectors represent directed line segments in space, while scalars denote only a magnitude without direction. Combining these distinct mathematical entities in a meaningful way contradicts the very nature of vectors and scalars. Thus, the correct answer is "No," as adding a scalar quantity to a vector quantity lacks both mathematical and conceptual coherence.
Therefore the correct option is option b.