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Intro to vectors and scalars

INT‑3.A (EU)
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Scalars and vectors are two kinds of quantities that are used in physics and math. Scalars are quantities that only have magnitude (or size), while vectors have both magnitude and direction. Explore some examples of scalars and vectors, including distance, displacement, speed, and velocity. Created by Sal Khan.

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  • blobby green style avatar for user vineeth.konavoor
    Does vectors have a location in space? does it vary with time?
    This is a question from my Physics textbook. I even couldn't understand the question. Can you explain and answer me?
    (227 votes)
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    • aqualine tree style avatar for user Dima
      A vector stores only two parameters of information - length and direction. It doesn't tell you anything about it's origin/location. It can vary with time if it's given as a function of time, for example if the vector symbolises speed of an accelerating object, then it does vary on time, if the speed is constant then it doesn't vary on time.
      (289 votes)
  • blobby green style avatar for user Apoorv
    Why and how is displacement equal to final position minus initial position?
    (72 votes)
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    • mr pants teal style avatar for user Dustin
      Say you are running a 50 mile marathon but you start at the 30 mile mark.
      Your displacement from your start (30 mile mark) to the finish (50 miles) would be 20 miles. instead of counting each mile from the mark in which you started you can simply subtract the number from which you started from the number in which you end to get the total displacement.
      (30 votes)
  • hopper happy style avatar for user Sandra Tang
    What is the triangle symbol at ?
    (39 votes)
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  • blobby green style avatar for user nehadhillon5
    What is the difference between distance and displacement?
    (12 votes)
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    • mr pants teal style avatar for user Moon Bears
      Distance is how far you go, displacement is how far you went relative to your starting position! Example: If I walk 2 miles from my house to the grocery store, and walk 2 miles back to my house, my distance traveled is four miles; however my displacement is zero because I'm back where I started.
      (53 votes)
  • marcimus pink style avatar for user Emily Adam
    A scalar value cannot be a vector because it does no include direction, but can vectors be considered scalar?
    (21 votes)
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  • starky ultimate style avatar for user ST
    If people developed the ability to time-travel, would time be a vector or a scalar quantity?
    (13 votes)
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  • leaf yellow style avatar for user Mohd. Nomaan
    O.K. so on earth we can say that an object is going with velocity v(direction North To South). But what I have learned now is that every point in the universe is the centre of universe.
    so question 1
    Is this true?
    question 2
    if yes than how will you define direction of a particle. I mean that everywhere you are going in the universe you are at the centre of it.
    (10 votes)
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    • leaf blue style avatar for user Matthew Daly
      Deep questions!

      1) Yes, that is a concept from relativity called reference frames. Einstein theorized that the laws of physics should all work no matter what object you think marks the center of the universe, and all experiments up to this point have agreed with him.

      2) In a theoretical sense, the vectors you're seeing exist in Euclidean space, which does have a well-identified center (the origin). If someone is doing real-world problems, what you'll find is that they will (usually without mentioning it) assume that there is a standard frame of reference. For instance, if I want to talk about a person running around a circular track, I would assume that the origin is the spot where the person started running. In practice, you'll probably find that it isn't as confusing as you might fear.
      (18 votes)
  • winston baby style avatar for user Subhashree Sadangi
    how is force a vector quantity?
    (7 votes)
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    • leaf grey style avatar for user patoof
      Force is a vector quantity as it has both size and direction.
      Force can make an object move in a particular direction, A force can act up, down, against motion etc.. For example air resistance, or the normal force on an object, or tension and many others.
      (15 votes)
  • leaf blue style avatar for user AwesomeShweta
    Can a vector have zero component along a line and still have non zero magnitude?
    (6 votes)
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  • male robot johnny style avatar for user Potato
    What is the name for a quantity with only direction?
    (7 votes)
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Video transcript

What I want to do in this video is talk about the difference between vectors and scalars. And they might sound like very complicated ideas, but we'll see over the course of the videos that they're actually very simple ideas. So first I'll give you a little bit of a definition. And then I'll give you a bunch of examples, and I think the examples will make things super clear. Hopefully, they'll make things super clear. A vector is something that has a magnitude, or you could kind of view that as a size, and it has a direction. So "and" it has a direction. A scalar only has a magnitude, or size. And if that doesn't make sense to you, it will hopefully make sense to you in a second when I show you an example. For example. Let's say that I have, let's say that that's the ground-- let me do the ground in a more appropriate ground-like color. So this is green right over here. And let's say that I have a brick here. I have a brick on the ground. And I pick up that brick, and I move it over to this place right over here. So I move the brick right over there. And then I take a ruler out, and I say, wow, I've moved the brick 5 meters. So my question to you, is my measurement of 5 meters, is it a vector or a scalar? Well, if I just tell you 5 meters, you just know the size of the movement. You just know the magnitude of the movement. So if someone were to just say 5 meters, this is a scalar quantity. And when we're referring to moving something, or how much something has, I guess, changed its position, and I don't give you the direction, we're talking about distance. And I'm assuming you've heard the word distance. How far of a distance has something traveled? So this is distance. So we could say that this block, or this brick, because of my picking it up and moving it, has moved a distance of 5 meters. But if I didn't show you this picture here, and someone just told you that it moved a distance of 5 meters, you wouldn't know if it moved to the right 5 meters, you wouldn't know if it moved to the left 5 meters, if it moved up or down or in or out, or-- You don't know what direction it moved 5 meters. You just know it moved 5 meters. If you want to specify that, so, we could say that this brick right over here, that it moved 5 meters to the left. Now we have specified a magnitude, right over there. So that is a magnitude. And we have specified a direction, to the left. So you now explicitly know that they went 5 meters to the-- oh, sorry. It should be 5 meters to the right. Let me change that. So, 5 meters to the right is what it got moved. It started here and went 5 meters to the right. So once again, the magnitude is 5 meters, and the direction is to the right. So what I've just described to you right here is a vector quantity. So this, all of this business right over here, this is a vector. And when you talk about the movement, the change in position, and you give its direction, the vector version of distance, I guess you could call it, is displacement. So this right here is displacement. So the correct thing to say, you would say that this brick has been displaced 5 meters to the right, or it has been moved a distance of 5 meters. Distance is a scalar quantity-- I didn't tell you what direction we moved it in. Displacement is a vector quantity. We told you that it is to the right. Now let's explore this if we talk about the actual, well, we'll talk about the speed or velocity of something. So let's say that this 5 meters was traveled and let's say that the change in time-- let me just, because you're probably not familiar with what that means. So let's say that the change in time right here, when I moved this block 5 meters, let's say that it was, I don't know, let's say that the change in time was 2 seconds. So maybe right when the block started moving, maybe on my stopwatch it said 0. And then on my stopwatch when it stopped moving, it said, or when it got to this position, I should say-- when it left from this position, my stopwatch said 0. When it got to this position my stopwatch said 2 seconds. So the change in time, or the duration we're dealing with, is 2 seconds. And this is, for all we know, time only goes in the positive direction. So you could assume that it's, you could pick that as a vector or a scalar quantity, I guess, because there's only one direction for time, as far as we know, or at least in what we're going to deal with for the simple physics. So what is a measure of how fast this thing moved? So, how fast did this thing move? So we could say it moved 5 meters in 2 seconds. Let me write this down. So it moved 5 meters per 2 seconds. Or we could write this as 5/2 of a meter per second. Or 5 divided by 2 is what? 5 divided by 2 is 2.5 meters per second. This right here is just the 5 divided by 2, let me make that clear. That right there is just the 5 divided by the 2. So my question to you. This 2.5 meters per second tells you how far it traveled in a certain amount of time. Is this a vector or a scalar quantity? It is telling you how fast it went, but is it giving you just a size of how fast it went? Or is it also giving you direction? Well, I don't see any direction here. So this is a scalar quantity. And the scalar quantity for how fast something is going is speed. So we could say that the speed of the brick is 2.5 meters per second. Now, if we do the same calculation, and we say it went 5 meters-- I'll just write m for meters-- to the right in 2 seconds, then what do we get? We get 2.5, once again, 2.5 meters per second-- I'll just abbreviate them as meters per second-- to the right. So is this a vector or a scalar quantity? I'm telling you the magnitude of the speed, that's right here. This is the magnitude, 2.5 meters per second. And I'm also telling you the direction, to the right. So this is a vector quantity. This is a vector quantity. And when you specify both the speed and the direction, so the 2.5 meters per second is a scalar, and the direction, you are talking about velocity. You are talking about velocity. So an easy way to think about it, if you're thinking about change in position and you specify the direction of the change in position, you're talking about displacement. If you're not talking about the direction, you want the scalar version, you're talking about distance. If you're talking about how fast something is going, and you give the direction that it's going in, you're talking about velocity. If you don't give the direction you are talking about speed. Hopefully that helps you a little bit. In the next video, we're going start working with these a little bit to start solving some basic questions about how fast something is going, or how far it might travel, or how long it might take it to get someplace.