vectors versus scalers what are they what is the difference between a vector and a scalar and how do we represent vectors in this video we will be looking at all of these things and more I'm a smart sense I do physics chemistry and math videos so please make sure to subscribe if you haven't already if you're learning about vectors and scalers you are most likely moving into the mechanics section of physics the section of mechanics deals with matter and motion among this matter or materials or objects it also deals with forces and energy and the effect of these things on the objects on the bodies themselves so starting at the beginning what on Earth is a vector what is a scalar and what is the difference both vectors and scalars are physical quantities now what is a physical quantity physical quantity is a physical property or quantity that can be measured using numbers for example if I am recording the temperature if I'm looking at length it if I'm looking at distance if I'm looking at Mass if I'm looking at time these are all things that we refer to as physical quantity physical quantities have an amount this is what we call a magnitude and they have a unit a scalar is a physical quantity that has magnitude only now magnitude remember is the size the amount for example if I want to give my height I will say that I have a height of 155 centimeters 155 this amounts this quantity this value that is what we call magnitude it's just an amount so scalars have only magnitude they do not have a Direction so for example if I want to say that a car was traveling at five meters per second this is what we call speed and speed is also a scalar speed has no Direction examples of scalars include the following Mass distance time speed power work energy charge you will deal with some of these in grade 10 and others in grade 11 and in grade 12. vectors on the other hand can be defined as physical quantities that have both magnitude and Direction so for example if you've done a calculation and you've worked out the velocity of a vehicle and you answer by saying the velocity of the vehicle was 120 kilometers per hour your teacher is going to mark that answer incorrect because you did not state a direction your answer would be as follows the velocity of the car is 120 kilometers per hour to the right or in the positive direction or something like that Vector examples include the following we've got weights which is measured in Newton it's actually a force displacement which is measured in meters velocity which is measured in meters per second acceleration which is measured in meters per second per second Force which I as I mentioned is measured in Newton momentum kilograms per meters per second impulse Newton seconds electric field Newton per second not all of these vectors will be dealt with in grade 10 but it's important to be able to list or give me some examples of vectors these are examples of vector quantities because not only do they have magnitudes and remember magnitude is the amount or the quantity itself so 5 Newton three meters but both of these have a direction allocated to them as well if I had to give you these two physical quantities one being two meters per second East and the other one being two meters per second and I had to ask you to classify them as vectors or scalars I hope you can see that the 2 meters per second because it just is a magnitude and no direction this is a scalar and the two meters per second East because it has a magnitude and a direction it is a vector this is a measure of speed and this is a measure of velocity now some Learners often get confused because they think that speed and velocity are different things the magnitudes are the same so for example if I tell you I am going to travel now and I'm going to jog and I give you my speed as 2 meters per second I can also say that my velocity was 2 meters per second East I'm telling you almost the same information but when I'm quoting my velocity I'm giving you a little bit more information by giving you the direction when using equations of motion like this one which we will be doing in another video a lot of Learners think that because v i and v f stand for velocity initial or initial velocity and VF meaning final velocity that you cannot use this equation to calculate speed that's not true although v i and b f stand for velocity remember speed is basically velocity but just without the direction so for example in grade 12 when we do vertical projectile motion you may use this formula to calculate speed your answer will not have a direction because the question asks for Speed but essentially you are calculating a very similar physical quantity we can represent vectors graphically and we do this by using an arrow the length of the arrow represents the magnitude of the vector so if I draw a little short Arrow I'm referring to a relatively small magnitude whereas if I draw a very large or very long Arrow I'm referring to a larger magnitude vectors have a direction the direction of the arrow indicates the direction of the vector if I have a scenario where I have a person pushing a box to the right and I tell you that this person is pushing with the force of 5 Newton the first thing you have to remember is that force is a vector which means it requires a direction and it also means I can represent it visually by using an arrow so let's say this is my Force Vector representing 5 Newton to the right now I tell you that the person is pushing in the same direction but with double the force how we could now represent that Vector is with an arrow that is double in size I know mine's not exactly double but let's pretend an arrow that is double in size but also pointing to the right so you can see here that the size of my arrows is important if we compare this to a person pushing in the opposite direction now to the left you will see that these vectors no longer satisfy what is going on in this diagram the person is pushing in the opposite direction we can no longer Point our Force Vector to the right as we did with this person we will have to change the direction of our Vector because the person is now pushing to the left you also need to understand properties of vectors if I have two arrows of exactly the same size pointing in the exact same direction these are called equal vectors if I had to rotate this Vector let's say 90 degrees like that these are no longer equal vectors because although they have the same magnitude they're still the same size this Vector is now pointing in a different direction and remember it's both the magnitude and the direction that makes up the vector so these are not equal vectors anymore these are also not equal vectors because again although they're the same size they're the same magnitude they're pointing in the opposite direction and what this would be an example of is a situation such as this let's pretend that I have this person person a pushing to the right this would be the vector that represents that Force this person over here person B pushing with the same magnitude of force but to the left that would be this Vector representation over here and although the magnitudes are the same they're in opposite directions but what do you think is going to happen to that box now remember both of these people person a and person B are pushing with the same magnitude over all the force is zero why because if I'm pushing with five Newton that way and five Newton that way overall the box is not going to move we will be discussing net vectors in the next video but for now you need to know that an arrow is used to graphically represent vectors if a question tells me that to the east is my positive direction or to the right is my positive direction and I have two vectors acting let's say I have a vector acting that way to the right A little I have a vector acting this way to the left what's important to note is that this would be a positive vector and this would be a negative Vector just because it's acting to the left now that doesn't change the fact that its magnitude will be say for example 5 Newton and 5 Newton see they're equal in length so say this one's five Newtons to the right 5 Newtons to the left this one we call a negative Vector simply because in this question I mentioned to the right or east as being positive and this one's going in the opposite direction it's going in the negative Direction in the next video we will be looking at what a resultant Vector is and how to calculate a result in Vector but for now let's do two past paper questions very quickly based on this video which one of the following combinations include two scalar quantities and one vector quantity we can do this by process of elimination a displacement as a vector acceleration is a vector so immediately we know it's not a because we're looking for one vector quantity in B we see speed that's a scalar velocity is a vector and distance is a scalar so that matches the question because two scalars being speed and distance and one vector which is velocity C is incorrect because it's got two Vector quantities force and acceleration D is incorrect because all of those are vectors our next question which one of the following physical quantities is a vector distance is a scalar mass and time are both scalars so therefore answer is displacement which is a vector foreign