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Question Video: Understanding How Scalar Quantities Relate to Direction Science

Which of the following does not correctly explain how scalar quantities relate to directions? [A] Scalar quantities include those for which a direction is meaningless. [B] Scalar quantities include those that have no particular direction. [C] Scalar quantities include those that have a particular direction.

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Video Transcript

Which of the following does not correctly explain how scalar quantities relate to directions? (A) Scalar quantities include those for which a direction is meaningless. (B) Scalar quantities include those that have no particular direction. Or (C) scalar quantities include those that have a particular direction.

Let’s start by recalling a definition of scalar quantity. A scalar quantity is a quantity which is fully defined by a magnitude and a unit. We can compare this to a vector quantity, which is a quantity that is fully defined by a magnitude, a direction, and a unit. The length of this line is an example of a scalar quantity. It can be defined by just a number and a unit, 10 centimeters, for example.

This arrow, on the other hand, is not very well described by a scalar quantity. We could say that the magnitude of the arrow is its length. But it also has a very clear direction associated with it. This is why we use arrows to represent vector quantities. We could say that the arrow represents, say, a displacement of 10 centimeters to the right. This makes displacement a vector quantity. It includes information about direction as well as having a magnitude.

Now we’ve defined these two terms, let’s take another look at the statements we’ve been given. Statement (A) says that scalar quantities include those for which a direction is meaningless. This statement is correct. For example, consider temperature. It only makes sense to describe the temperature of a beaker of water in terms of a magnitude and a unit, for example, 60 degrees centigrade. We would never say that it had a temperature of 60 degrees centigrade upward or 60 degrees centigrade south. Temperature is a scalar quantity, and assigning it a direction is meaningless.

Remember, the question is asking us which of these statements does not correctly explain how scalar quantities relate to directions. Since statement (A) is true, this means it is not the answer to the question.

Let’s now take a look at statement (B). Scalar quantities include those that have no particular direction. Now, this statement is also true. As another example, let’s think about the distance between two places. For example, we could say that the bank is at a distance of two kilometers from our house, without indicating the direction we’d have to walk in to get there. This means that distance is a scalar quantity.

Now, in this situation, a direction wouldn’t be completely meaningless. We could talk about the direction we’d have to walk in to get from our house to the bank. But the distance itself is still just two kilometers. Distance is a scalar quantity, and it has no particular direction. This means that statement (B) is correct. So it’s not the answer to the question.

So we find that the only incorrect statement is statement (C). Scalar quantities include those that have a particular direction. Now, this is not true. If a quantity has a particular direction, then it must be a vector quantity. For example, if we described the bank as being two kilometers east from the house, then this would in fact be an expression of a vector quantity called displacement, rather than the scalar quantity called distance.

So option (C) is the final answer to our question. The statement “Scalar quantities include those that have a particular direction” does not correctly explain how scalar quantities relate to direction.

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