Answer:
(a) No. Only two such scalars can be added which represent the same physical quantity.
(b) No. A scalar cannot be added to a vector even of same dimensions because a vector has a direction while a scalar has no direction e.g., speed cannot be added to velocity.
(c) Yes. We can multiply any vector by a scalar. For example, when mass (scalar) is multiplied with acceleration (vector), we get force (vector) i.e., .
(d) Yes. We can multiply any two scalars. When we multiply power (scalar) with time (scalar), we get work done (scalar) i.e., W = Pt.
(e) No. Only two vectors of same nature can be added by using the law of vector addition.
(f) No. A component of a vector can be added to the same vector only by using the law of vector addition. So the addition of a component of a vector to the same vector is not a meaningful algebraic operation.
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