00:02
Now, in this problem, we are given with this figure and here this is the u vector that makes an angle 60 degree in the counterclockwise direction from the positive x and this is the v vector.
00:14
Now, we have to find the components of u plus v vector and u minus v vector.
00:25
Now, here we can see that the magnitude of v and u vector is 1 because the radius of the circle is 1, r is 1 unit here.
00:33
So, let's first write the vector in component form.
00:38
Then we are going to evaluate these two things, u vector plus v vector, u vector minus v vector.
00:44
Okay, so u vector, this would be equals to r cosine theta, this would be the x component, so i can write x cap here, the unit vector along the x direction plus r sine theta, y cap.
01:01
Right, now r is 1 here, so 1 cosine theta, we have 60 degrees, x cap plus 1 sine 60 degrees, y cap.
01:13
Now, we know cosine 60 degree is 1 over 2, so 1 over 2 x cap plus this would be square root 3 over 2 y cap.
01:23
So, this is u vector.
01:26
Now, i can write the v vector.
01:32
So, this would be r cosine theta x cap plus r sine theta y cap.
01:38
But this time, theta would be different.
01:41
This angle would be the theta and this would be 30 plus 180.
01:47
Theta would be 30 degree plus 180 degree.
01:50
So, that is 210 degrees.
01:53
So, i can plug it here, r is 1, cosine 210 x cap plus 1 sine 210 y cap.
02:04
So, this would be equals to cosine 210 degree is minus square root over, square root 3 over 2 x cap...