00:01
In the question, there are three vectors.
00:04
So in order to find the angle between two vector, we have to use a formula.
00:11
Let's first of all remember what is the formula.
00:14
Let's say this is vector a and this one is vector b and this one is b.
00:21
So the angle between them is theta.
00:24
So we have a formula for theta, which is the cosine of the theta.
00:31
Cosine of theta is equal to that product of the vectors a and b and divided by their magnitudes.
00:41
So the multiplication of their magnitudes, which is absolute value of a times absolute value of b.
00:48
In this case, be careful.
00:50
I can just write absolute value of a or magnitude of a, something like this one.
00:57
So that doesn't matter.
00:58
Use two dash or one dash that doesn't matter so let's leave theta alone which is the cosine inverse of the cosine function and a times b divided by absolute value of a times absolute value of b so this is the formula that we are going to use for each of the vectors so in the first one so what i need i need the dot product of the vectors a and b let's say it is the theta between angles, say between two vectors a and b.
01:32
The angle is theta.
01:34
So the dot product of a and b, which is i'm going to multiply the x values of the vectors each other and then plus the multiplication of the y values plus and multiplication of the z values.
01:52
So the x values of the vectors a and b are 1 times 3 and plus 1 times 2 and plus 0 times 1 which is it is 5 and the magnitude of the vector a which is squared of the square of the each values so which is 1 squared plus 1 squared plus 0 squared which is squared of 2 and the magnitude of the b which is squared of let's say 3 squared plus 2 squared plus 2 1 squared which is a square of 14 so from these and also let's find the magnitude of c which is squared of 1 squared plus 0 squared plus 2 squared which is square of 5 so the angle between a and b let's say it is theta so i'm going to use theta so i'm going to find theta by using the formula which is cosine inverse function and multiplication of a times we be which is five divided by the multiplication of their magnitudes which are squared of two times squared of 14 so we have to use calculator in this case so if you just plug in these values into the calculator and we will find um 19 point 10 degrees so so this is the angle theta, which is between the vectors a and b...