Practice: Components of vectors from endpoints. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video 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. 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. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript A vector is something that has both magnitude and direction. Magnitude and direction. So let's think of an example of what wouldn't and what would be a vector.
So if someone tells you that something is moving at 5 miles per hour, this information by itself is not a vector quantity. It's only specifying a magnitude.
We don't know what direction this thing is moving 5 miles per hour in. So this right over here, which is often referred to as a speed, is not a vector quantity just by itself. This is considered to be a scalar quantity. If we want it to be a vector, we would also have to specify the direction.
So for example, someone might say it's moving 5 miles per hour east. So let's say it's moving 5 miles per hour due east. So now this combined 5 miles per are due east, this is a vector quantity. And now we wouldn't call it speed anymore. We would call it velocity. So velocity is a vector. We're specifying the magnitude, 5 miles per hour, and the direction east.
But how can we actually visualize this? So let's say we're operating in two dimensions. And what's neat about linear algebra is obviously a lot of what applies in two dimensions will extend to three. And then even four, five, six, as made dimensions as we want.
Our brains have trouble visualizing beyond three. But what's neat is we can mathematically deal with beyond three using linear algebra. And we'll see that in future videos. But let's just go back to our straight traditional two-dimensional vector right over here. So one way we could represent it, as an arrow that is 5 units long.
We'll assume that each of our units here is miles per hour. And that's pointed to the right, where we'll say the right is east. So for example, I could start an arrow right over here.
And I could make its length 5. This applet also shows the coordinates of the vector, which you can read about in another page. The magnitude and direction of a vector.
The two defining properties of a vector, magnitude and direction, are illustrated by a red bar and a green arrow, respectively. More information about applet. There is one important exception to vectors having a direction.
Since it has no length, it is not pointing in any particular direction. There is only one vector of zero length, so we can speak of the zero vector.
We can define a number of operations on vectors geometrically without reference to any coordinate system. Here we define addition , subtraction , and multiplication by a scalar. On separate pages, we discuss two different ways to multiply two vectors together: the dot product and the cross product.
Recall such translation does not change a vector. The vector addition is the way forces and velocities combine. For example, if a car is travelling due north at 20 miles per hour and a child in the back seat behind the driver throws an object at 20 miles per hour toward his sibling who is sitting due east of him, then the velocity of the object relative to the ground!
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