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This video is about vectors and scalers. We will start by discussing the difference between

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vectors and scalers. Then we will see how to represent, add and subtract vectors, and we

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will finish with talking about the resolution of vectors into perpendicular components.

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Let's see what vectors and scalers are. A scalar is a quantity that has magnitude, but

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no direction, and the vector is a quantity that has both magnitude and direction.

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For example, if I say that I'm walking at 5 kilometers per hour, I am using a scalar

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because I'm only providing a magnitude, 5 kilometers per hour. On the other hand, when I say

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that I'm walking east at 5 kilometers per hour, I am using a vector because I'm using

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magnitude, 5 kilometers per hour, and the direction east. You will come across many scalers

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and vectors in physics. Let's see a few examples of each. Math, time, distance, temperature,

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and speed are all scalers. In our example, 5 kilometers per hour is speed. While force, acceleration,

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displacement, magnetic field strength, and velocity are all vectors. When I say that I'm walking

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east at 5 kilometers per hour, I am talking about my velocity. Let's see how vectors are represented.

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Vectors are represented by arrows like this, or maybe like this. We often write the name of the vector

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next to it. For example, A, and to show that this is a vector and not a scalar, we can add

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an arrow on top. In textbooks, vectors are often represented with letters written in bold.

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We can also write the value of the quantity represented by the vector next to the vector.

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So, for instance, if this is a force vector, representing three new tons, I would write

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three new tons next to it. Note that the magnitude represented by a vector is proportional to its

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length. So, if I want to draw a vector that represents a force of six new tons, it would

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have to be twice as long as the three new tons vector. Next, let's discuss graphical vector

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addition and subtraction. We are going to work with vector A and vector B. Let's see how to add

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and subtract these vectors. There are many different methods for vector addition and subtraction.

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Here, I will just show one of these. To add A and B, I will redraw the vectors, placing the

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starting point of B at the end point of A. Based on the definition of vector addition, A plus

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B is this vector. Let's see subtraction. Here, I will redraw the vectors again, but instead of

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B, I will draw a negative B at the end point of A like this. So, the black vector is still

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A, but the blue vector here is negative B, because it has the same magnitude as B, but points

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in the opposite direction. So, using vector addition, this vector here is a plus negative B, which

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is the same as A minus B. Finally, we will see hat result vectors into perpendicular components.

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To do so, we will use this diagram and formulae. Let's see two examples. In the first one,

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we will resolve A into a horizontal and a vertical component and find the magnitude of these components.

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The horizontal component looks like this and the vertical component like this. Using the

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formulae, below the diagram in the blue box, for AH, the horizontal component, we get

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the magnitude of A, which is 5, times cosine of the angle, and this is 30 degrees. This gives us

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approximately 4.33 centimeters. For AV, the vertical component, we get 5 times sine 30, which is equal

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to 2.5 centimeters. In example, 2, and object rests on a slope, and we have to find the magnitude

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of the component of the objects weight that acts perpendicular to the slope. Let's start

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by drawing this situation. The slope looks like this, and here is the object resting on the slope.

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The weight of the object is pointing downwards. Let's resolve this weight into two components,

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one parallel and one perpendicular to the slope. The parallel component looks like this, and

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the perpendicular component looks like this. Due to the symmetry in the diagram, this angle

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here is also 20 degrees. I won't go into the mathematical details of why this is so here.

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Let's use the diagram in the blue box on the right. Imagine rotating the three vectors from the

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diagram that we have drawn until vector W lines up with vector A. Doing this, you should see that

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our purple vector lines up with AV, and our red vector lines up with age. In other words,

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the red vector corresponds to age. The red vector is the perpendicular component of the weight,

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and now we can calculate this magnitude, using the formula for age. So for the perpendicular

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component, we get the magnitude of the weight, and since the mass of the object is 10 kilograms,

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its weight will be 10 times the gravitational acceleration, so 10 times 9.81, which is 98.1

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Newton's. If this is not fully clear at the moment, don't worry. For now, just focus on understanding

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the work that we do with the vectors. So for the perpendicular component, we get 98.1 times

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cosine 20 degrees, and this is approximately 92.2 Newton's. Let's summarize what we have learned.

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To start, we looked at the definition of scalars and vectors. We mentioned that you will come across many

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scalars and vectors in physics, and we listed a few examples for scalars and vectors.

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We saw that vectors are represented by arrows, and that the magnitude of the quantity that

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the vector represents is proportional to the length of the vector, and we discussed that to add

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and subtract vectors graphically, we should place one vector at the endpoint of the other.

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Finally, we saw two examples of resolving vectors into perpendicular components, where

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we used this formula. And we have concluded our learning about vectors and scalars.

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With this video, we have wrapped up subtopic 1.3. In the first video of subtopic 2.1 motion,

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we will discuss distance and displacement.