Intro to Vectors and Scalars - Nerdstudy Physics

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Intro to Vectors and Scalars! Vectors are quantities that have both a magnitude and a direction. Let's learn all about it in this lesson!

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So, what is a vector? Well, vectors are mathematical quantities that are fully described by a magnitude and a direction. What do we mean by magnitude? That’s really just the size or quantity of something. It could be the length of a distance, the weight of an object, or even the amount of money you have in your bank account. If you can have more or less of something, if it can be measured on a scale, or if it can be bigger or smaller, [Pause] then it has a magnitude.

And what about direction? Well, that’s simple. Examples are right and left, up and down or even east and west, as well as north and south. It’s an indication of how something is oriented in space.

In mathematics, variables that are vectors usually have an arrow on top of them. So, if the variable ‘v’ were a vector, we’d put an arrow above it, like this, to represent that it IS in fact a vector quantity.

In physics, when we are given things that can be measured such as distance, time and speed. We define these measurable properties as physical quantities

Great!

So here’s a simple example of a vector. Suppose a friend is asking how to get to the grocery store and we tell them, “It’s half a kilometer north of here”. At a glance, it might look like we just gave them 1 piece of information telling them where to go. But, in reality, it actually consists of two pieces of information. First, we told them it’s half of a kilometer from here. Second, we also mentioned that it’s north of here. The first piece of information was the distance. It can be bigger or smaller; it’s a quantity. In other words, a magnitude. The second piece was obviously the direction. And hey, remember what a vector is? Something that has magnitude and direction. So when we said, “It’s half a kilometer north of here”, we were really giving our friend the vector 0.5 km north!

Awesome!

Alright, now say another friend comes to visit, and they notice you’ve got 42 books on your bookshelf. The number of books you have - is it considered a vector quantity?

Well, the answer is no. See, even though there’s a magnitude involved, and even though you can have more or less books, there’s no direction here. Therefore, it is not a vector since vectors must involve a direction. In fact, quantities that involve a magnitude but no direction are called scalars.

Here’s a fact that might come in handy: every vector has a scalar associated with it. And this makes sense, because a scalar quantity is one with only magnitude. But a vector involves a magnitude as well as a direction. So, we can actually think about a vector as a Scalar quantity that also involves a direction.

In fact, there is even a special way to indicate the magnitude of a vector. And that is, for any vector ‘v’, we denote its magnitude by putting two lines on either side of it, like so. And like we mentioned earlier, this arrow denotes that it's a vector.

Good!

Let’s go over one last example. We go online, check the weather, and find that the wind is blowing south at 30 kilometers an hour. Would this be considered a vector quantity?

Well, of course it is! And why? Well, that's because it contains a magnitude which corresponds to the speed of the wind. The wind could be faster or slower. and it also tells us where the wind was blowing; in other words, the direction of the wind. Again, magnitude and direction together give us a vector.

Awesome!

And that brings us to the end of this video! Now we know what a vector quantity is. It’s simply any mathematical quantity that involves both a magnitude and a direction. We also briefly went over what a scalar quantity is and how it is a quantity that only represents magnitude. In the next lesson, we’ll learn how to mathematically represent vector quantities, so, until next time, have a good one!