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Current time:0:00Total duration:2:38

- [Instructor] We're told
that particles A and B are moving along a plane. Their velocities are
represented by the vectors, vector a and vector b respectively. Which option best describes the meaning of the following statement. Choose one answer. So pause this video and try to
work through this on your own before we work through this together. All right, now let's work
through this together. So this is saying that
the magnitude of vector a is equal to the magnitude of vector b. So we know that a vector is specified by both a magnitude and a direction. And this is just saying that
the magnitudes are the same. So for example, vector
a could look like this, and vector b could look like this. It could do something like that where it has the same magnitude
and the same direction. Or vector b might be in a
completely different direction. The magnitudes being
equivalent just tells us that the length of these
arrows are the same, but we could have
different directions here. So what this tells me is
that we have the same speed which is the magnitude of velocity, but not necessarily the same direction. Now let's look at the choices here. The first choice is
that two particles move at the same speed and
in the same direction. So we've already said that
that's not necessarily the case. In order for choice A to be correct, they would essentially have
to be equivalent vectors. Choice A would be the case
if we said that vector a is equal to vector b, then they would have to
have the same magnitude and the same direction, the same magnitude and the same direction. But that's not what they told us. They just told us that the
magnitudes are the same, not necessarily the directions. So I'll rule that one out. The two particles move at the same speed, but not necessarily in the same direction. Yes, that's what we just talked about. They have the same speed, which is the magnitude of velocity, but they didn't tell us
anything about the direction, just the magnitudes. So I like this choice, but
let's look at choice C. The two particles move
in the same direction, but not necessarily at the same speed. Well, we know they move at the same speed. That's what this is telling us. The magnitudes are the same. We just don't know anything
about the direction. So I would rule this one out as well. In order for choice C to be the case, you would see something like this, maybe that is vector a right here, and then vector b would
move in the same direction, but it would have a different magnitude. And here you would visualize the magnitude as the length of the arrow. But that's not what they told us. They told us this right over there.