00:01
Hello, welcome to this lesson.
00:02
In this lesson for the first part, we will calculate the scalar product of vector a and vector b, given that the magnitude of vector a is 7, magnitude of vector b is 9, and the angle between them is 60 degrees.
00:18
So usually we have the cost of the angle between the two vectors, which is equal to a dot b on the magnitude.
00:29
The product of their magnitude so we'll have the a dot b which is equal to the magnitude the product of the magnitude of the two vectors cos of the angle so here we are giving that the magnitude of vector a is 7 so let me actually have it like this then that for b is 9 that we have course of the angle 60 degrees so we have a dot b which is equal c now we have 7 times 9 which is 63 and we have course of the angle theta which is 0 .5 or 1 and 2 so here we have a dot b which is equals to 31 .5 all right now let's move to the b part where we have a para little abcd so here we are looking at the angle at b all right so we need to look at the a b so if this is b we're essentially looking at the angle between these two vectors bc and b a all right so here let's find the a b right which would be b minus a so with this we'll have the one negative two and three we are subtracting zero one and two so we have this which will be equals 1 minus 0, that's 1.
02:38
We have negative 2 minus 1, that's negative 3.
02:43
We have 3 minus 2, that's 1, all right? then again, we look at the bc, all right? so it goes this way so that we can find the angle between them...