00:01
Problem we have been given two vectors u and v and we need to find the angle between u and v now the angle theta between two vectors u and v is given by the formula cosine of u dot v divided by the modulus of u times the modulus of v so let us determine this so first of all we have the arc cosine of u .v.
00:35
So how do we obtain the dot product of two vectors? we find the sum of the products of the corresponding components.
00:41
So the x component of u is one to multiply that by the x component of v, which is negative one.
00:48
With this we add the x the y component of u, which is square root of three times the y component of v, which is the square root of three.
00:58
And in the denominator, first of all, we have the modulus of the vector u.
01:03
So that's, that will be the square root of the sum of the squares of the components.
01:06
So the square root of one squared plus the square root of three squared.
01:11
Similarly, the modulus of the vector v will be negative 1 squared plus square root 3 squared, and we take the square root of that.
01:20
So let's just calculate this.
01:24
So we have the arc cosine.
01:26
And over here we have negative 1 plus square root of 3 times squared of 3 is 3...