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Which one of the following statements is true concerning scalar quantities?

1) Scalar quantities must be represented by base units.
2) Scalar quantities have both magnitude and direction.
3) Scalar quantities can be added to vector quantities using rules of trigonometry.
4) Scalar quantities can be added to other scalar quantities using rules of trigonometry.
5) Scalar quantities can be added to other scalar quantities using rules of ordinary addition.

1 Answer

3 votes

Final answer:

The correct answer is that scalar quantities can be added to other scalar quantities using rules of ordinary addition. Scalar quantities have magnitude but no direction, unlike vector quantities that have both magnitude and direction.

Step-by-step explanation:

The question is asking about the properties of scalar quantities in physics. In the context of physics, scalar quantities are physical properties that are fully described by magnitude, but they have no direction. This is in contrast to vector quantities, which are described by both magnitude and direction and can be represented as arrows on a graph where the length indicates magnitude and the arrowhead indicates direction.

Regarding the options presented in the question, the true statement concerning scalar quantities is that scalar quantities can be added to other scalar quantities using rules of ordinary addition. This is because scalar quantities have only magnitude and no direction to consider when combining them.

When adding a scalar to a vector, you modify the magnitude of the vector by the amount of the scalar, but this addition does not follow the rules of trigonometry. Instead, rules of trigonometry are applied when adding or subtracting vector quantities, which involve magnitude and direction. Hence, the correct answer to the student's question is option 5).

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