About this video
Sal checks which of four choices can represent a vector, something with both a magnitude and a direction. The number 5 and the outcome of 5 + 5 give only a magnitude, and the angle 5 degrees gives only a direction, but the point (5, 5) can be the head of a vector from the origin, which has both.
You'll be able to
- state that a vector has both a magnitude and a direction.
- decide whether a number, an angle or a point can represent a vector.
- explain how a point can represent a vector starting at the origin.
Key words
- Vector
- A quantity with both a size (magnitude) and a direction.
- Magnitude
- How large something is, such as the length of a vector.
- Direction
- Which way something points, for example an angle from the positive x-axis.
Transcript
Voiceover:Which of the following can represent a vector? A vector is something that has both a magnitude and a direction. Let's see which one of these could represent something that has a magnitude and a direction. The first choice right over here is the number 5.
5 could represent a magnitude, you could say, essentially, how large something is. That's all the information has. It doesn't say 5 in a certain direction. This one by itself would not be a or it couldn't represent a vector. You need to specify a direction as well.
The angle measure 5 degrees. Well the angle measure 5 degrees could represent a direction. If you say it's 5 degrees. Let's say that's the positive X axis that's the positive Y axis. If you said it's 5 degrees relative to the positive X axis. If you said something like this, so if you had 5 degrees over there, that would be specifying a direction, but it's not giving us a magnitude.
It's not saying how far in that direction or how large in that direction. An angle measure of 5 degrees, you're giving us a direction, but no magnitude. Let's just cross these out. The point (5,5). Now this is interesting. If we say that the point is the end point of a vector that starts at the origin, so lets draw that out.
That's the positive X axis, positive Y axis. This is 1,2,3,4,5 in the horizontal direction. 1,2,3,4,5 in the positive vertical direction. The .5,5 is going to be right over there. If you said that this represents the head of a vector who's tail is at the origin.
The vector would look something like this. Now, you're giving both a magnitude and a direction. What's the magnitude? What's the distance between the origin and this point, right over here. You could solve using the Pythagorean theorem and the direction, it's this general direction.
This could specify a magnitude and a direction. This could represent a vector. The outcome of 5+5, obviously that's just 10. That's just a number. For the same reason, this first choice, if I just have a number, that could be a magnitude, but we don't have a direction as well.
This could not represent and that one could not represent a vector.
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