Scalar and Vector Quantities — Resolution of Vectors (Score 90+ in Physics) #jamb #physics #vectors

Transcript

Quantities with magnitude only. Yes, these quantities have as magnitude only. Examples of this are mass, time, temperature, speed, energy, so on. Yes. Length, area, volume, time, mass.

Let's take some daily examples of scalar quantities. Mass of a bag, 5 kilogram. Time spent watching this video 2 hours. Distance from home to school 3 kilometers. Speed of a car 10 km/h.

Temperature 30°C. When there's no direction involved, then you definitely know that that is a scalar quantity. More examples of scalar quantities. Energy, volume, density, power. Moving on to vector quantities.

Vector quantities are quantities with magnitude and direction. They have both magnitude and direction. Examples of vector quantities are displacement, velocity, acceleration, force, momentum, tension, thrust, electric field, magnetic field, E to C. Let's take some differences between vectors and scalar quantities. Scalas have magnitude only.

Vectors have both magnitude and direction. Number two, scalers have no direction. Vectors have directions. Directions. Number three.

Examples of scalers are speed. Why? Examples of vector are velocity. Yes, scalers have magnitude. Vectors have magnitude and direction. Scalas have no direction.

Vectors have both direction. Vectors have directions. Scalas have scalas examples are speed while vectors examples are velocity. Let's move on to the next. Vectors are represented with arrows.

Yes, arrows. The length of the arrow is the magnitude while the arrow head is the direction. Like this. The length, this length, this length is the magnitude while this arrow head is the direction. This is the direction.

This is the magnitude. Let's put it in cool form. The length from this place to this place is the magnitude. Why this arrow head here represents the direction. Also take note that the arrow is like bigger.

The vector is bigger. That is long arrows bigger vectors. In this case, this arrow head is showing the direction. Why this distance here is showing the magnitude of vector. Vector diagrams are shown using an arrow.

The length of the arrow represents magnitude direction of the arrow shows the direction. So we're just using I'm just using this diagram to qualify the representation of arrows in vector diagrams. Let's take a sharp example. A car moves 20 m east. Is this a scale or a vector? This is a magnitude and this is a direction.

So a magnitude and a direction equals a vector. Very simple. Vectors can be added using triangle law or the parallelogram law. Let's take a parallelogram law. This is when two vectors are joined tail to tail.

This is tail to tail. This part here is the tail to tail. the the completes the parallelogram and the resultant is found by drawing the diagonal. Let's look at the triangle. The triangular law is when the two vectors are joined head to tail.

Head to tail. Head to tail. And the law also draws the resultant vector by completing the triangle. When you have something like this to make it a triangular you have to complete it. The normal arrow here they are called the resultant vector.

This normal arrows here they the resultant vectors. Resultant vector. Resultant is the sum of this combined effect of two vectors. When we talk about the sum of combined effects that mean there will be something like the splitting of vector. So when we talk about splitting of vectors we talk that that splitting of vector is now when resolution of vector comes in.

We have resultant vector and we have resolution of vectors. What is resolution of vector? Resolution of vector means splitting one vector into two perpendicular components. the horizontal component and the vertical component. The horizontal component and the vertical component. When we look at vectors in the same direction, we see 6 Newton and 4 Newton gives us this direction.

10 Newton in this direction. and vectors in opposite direction 6 m/s 10 m/s in this direction there's a speed of 6 m/s and another speed of 10 m/s so the direction of the speed we go to where the 10/s is this direction there's a speed there's a force of 6 Newton year and another force of 10 newton here the resultant of the two forces will be in the in this direction of the 10 Newton force this direction. So component of a vector if a vector f makes an angle theta with the horizontal it will be a horizontal component f cos theta. Let's put it in writing. If a force F makes an angle theta with the horizontal, this will be F cos theta because it's in the horizontal.

Likewise, when it is in the vertical, F in the vertical vertical, it will be F sin theta. So let's bring okay result of two vectors two two forces are applied to a body as shown below. What is the magnitude and direction of the resultant force acting on the body this is the body here. So let's bring this diagram out properly. Would have something like this one here and the other one here.

So 12 Newton will be here and 5 Newton will be here. This place we have the angle theta. And this place we have our resultant vector 13 Newton. So A B C D. So I brought the diagrams properly to this place so we can easily access it without much obstructions.

So let's look at the solutions together. First let's we completed the first one. We completed the rectangle already. This rectangle as a whole here. This rectangle here.

And the diagonal of the parallelogram AC represents the resultant force AC. Where is AC here? This is the AC A here represents this 13 represent the resultant force. So that is done. The magnitude of the resultant is found using Pythagoras theorem on the triangle ABC. So the magnitude that we are supposed to look for we are supposed to find is the resultant of using Pythagoras theorem that means the magnitude here equals to AC.

Let's bring it out in a form. Magnitude equals to AC equals to the square root of of this five here and 12. [snorts] So 12² + 5² = to the square root of 144 + 25 equals to square root of [snorts] 169 equals to 13 new that's how we got this 13 new here so 13 newton AC here it will be 13 Newton here 13 Newton. So the direction of AC tan theta equals to when we bring 12 / 5 over 5. So we're looking for the theta.

Then we do the tan inverse of this 12 over 5 here and we get 67° 67°. Let's bring it here 67°. So we have gotten our magnitude to be 13 Newton and we have gotten our direction to be 67°. Attention is the only thing you have to pay to get this right. So let's move on to resultant of three vectors.

I'm trying to use this to get our attention and make us understand this concept as fast as possible. To get the to get the resultant here we square root 5 square + 5 square 5 square + 5 square = to 25 + 25 square root = to square t of 15 equals 7.07 Newton. So I've gotten the AC. Now let's get the tan theta of this this guy. The tan here t theta equals to 5 or should we do it in let's do it in a ne page.

So tan theta = 5 / 5. So tan theta equals to 1. Since we're not looking for tan theta, but we're looking for theta. So our theta will be inverse of 1. Tan inverse of 1.

tan inverse of 1 = to 45°. Yes. Let's start from here again. tan theta = 5. The next line tan theta = 1 and want to get the tan inverse of 1.

So we make theta the formula equals to tan inverse of 1 = 45°. I hope you got this. Tell me in the comment section below if this is clear to you. So let's take a real life example like let's take you like real life example. When you pull a load with a rope at a particular angle part of the force pulls it where upwards and part of that force again lifts the load towards you.

Let me come again. Part of the force pulls it forward and part of the force lifts it upwards. Let's take a quick example and see if we get what I've been pointing out since. A force of 100 Newton. Coming coming 100 Newton.

A force of 100 Newton act at an angle of 60. That's theta = to 60°. So the horizontal find the horizontal component. What will come straight to your mind is horizontal component f cos theta. Oh, I mean this is 10, not 100.

10. How do I erase it? 10 10 then 10 then 10 then 10 then 10 then 10 then 10 then 10 then 10 then 10 then 10 is not 100. So 10 cos 60 equals to 10 * cos 60 is definitely 0.5. So 10 * 0.5 will give us equals to 5 newton. So that is that's the force that acts at the angle 60 5 Newton.

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I'll paste on the screen now. So this is the number on the screen 07087247175 07087247175. You call or you send a message to this number on the screen. Earlier on I was talking about resolving a vector into perpendicular component. You can see it yourself here too that when a a vector into component we are the opposite to finding the resultant.

We usually resolve a vector into component perpendicular to each other. Here you use you are resolving them into x and y components. This is just a proof of how we calculate the magnitude of the perpendicular component. If a vector of magnitude V and makes an angle theta with the horizontal then the magnitude of the components are surely x = to v cos theta and y = v sin theta. In this place you can easily tell that this course is talking about horizontal.

This sign is talking about vertical component. Let's look at this diagram here. So let's look at this diagram quickly. So in this diagram you see that this is the vertical component V and this is the what horizontal component. So we say that the horizontal component is what? y = to v cos theta and the vertical component is y = v sin theta.

I mean the horizontal component is x = to v cos theta while the vertical component is y = v sin theta. So let's check the proof here. The proof here is cos theta = x / v which gives us x = v cos theta and the vertical component sin theta = to y / v which gives us y = to v sin theta. That's how we came across how we used to get y = v cos theta and y = to v sin theta. Let me come again.

Y is the horizontal component. Y is the vertical component. Y X is the horizontal component. I'm sorry for mixing that up. Y is the vertical component.

Y X is the horizontal component. And in the vertical component we use sin theta and while in the horizontal component we use cos theta. So let's quickly take this example again. Calculating the magnitude of perpendicular component. When we have a force of 15 Newton that acts on a box as shown below here, what is the horizontal component of the force? This is the box we are talking about here.

Horizontal component of the force look at this horizontal here. This part and this is the vertical here. This part. Let me use another marker so that it's not going to be confusing. Yeah.

So this is the horizontal component and this is the vertical component and this is the force acting on this boss box. So for the horizontal component here we have x equals to 15. This 15 here cos 60° we using cos because we are looking for the horizontal component. So x = to 15 * cos 60. So our x = to 7.5 Newton.

So I've gotten our horizontal component. Let's put it in this space. Our horizontal component equals to 7.5 Newton. So let's get our vertical component equals to 15 sin 60. We're using this sign because it is in the vertical component.

So v = to check your calculator and check what 15 sin 60 is. But my calculator is approximately 13 newton or 12.99 newton. But in physics most times it is advisable to leave your answer in three decimal places. But in this question, I think we asked to leave it in two decimal places. So we leave it at 12.99 Newton.

So So let's go to the next page. In summary, sign is for the vertical component and C is for the horizontal component. And we should never forget the directions. Vector is vector has um a composite direction. I mean like direction is composed while dealing with vectors.

And let's always remember that speed is not a vector. Velocity is a vector. Speed doesn't have a direction but velocity does. Scalas have magnitude only. Vectors have magnitude and direction.

Vectors are represented [snorts] with arrows. Vectors can be resolved using s and cos. And let's avoid mixing up sign and cost too. So if you understand this topic, I can tell you for sure that you have secure easy marks in this jam physics 2026. Thank you for watching.

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