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.
