# O Level Math / High School – Transformations – vector, translation, reflection

hello in this session we will look at vectors and transformations in an earlier session I’ve talked about vectors and talked about some of the ways that you use them right and I’ve talked about how a vector how you might think of it as an arrow pointing in a certain direction and then it is basically a quantity that tells you the length and that tells you that the magnitude that means the size and the direction and it can be used to describe anything that has a magnitude and direction like the force or displacements or velocity and so on and then you can describe a vector by two numbers one number be the magnitude right for example you can say that the magnitude of this is five and five can be the force and 5 Newtons of distance like five meters and so on and a direction but in the direction you might describe that you you will need a reference direction for example to the north and this might be a certain angle by 20 degrees so you can say that the direction is so many degrees to the north so that’s the vector now in this session we are going to look at another way of describing this same nation to describe the same information about the direction and and the angle and the way to do that is to think of a graph before X and y-axis okay if I on the graph you can imagine drawing an arrow or a vector with to tell them at the origin the tip of the arrow would be somewhere on the graph if you draw them then there is another way to you can tell you can describe a vector you can make use of the position that arrow the position of the temple that arrow on the graph so let’s say for example the x value is 4 and the y value of the point is 3 so in a sense the 4 and 3 is an equally good description equally good as the magnitude and the distance that means that if I if instead of telling you the magnitude and the angle I tell you the X and the y value of the graph paper then you can actually draw the same vector simply by going to that point and drawing the knife pointing from 0 to that points so the information using x and y is an equally good way to represent or to describe the vector it contains the same information you can convert between X Y and length and angle alright so that’s another way to describe a vector and in our last session I’ve talked about matrix now we can simply write this information 4 and 3 and arrange them in the form of a matrix so one way to do that is to write 4 comma three so that’s like matrix with two columns and one row another way that is also of abused is by writing for and as three below that okay and that’s a matrix with two rows and one column now