00:01
Okay, so let's solve the first exercise.
00:06
Okay, let's compute this guy.
00:10
The length of v plus 2 w squared is equal to what? the scalar product of v plus 2 w with itself.
00:28
So here what we get? we get okay the length of v plus four times the length the dot product between v and w plus four times the length of w okay now we we know that oh this one is length squared and squared okay, now we know that the length of v is 3.
01:09
So here we get 9 plus 4 multiplied by what? this one, the dot product is equal to the length of v multiplied by the length of w multiplied by cosine of pi over 4, which is 1 over square root of 2, plus four times the length of w squared which is 2.
01:40
Okay, so at the end what do we get? we get 9 plus 4 multiplied by the length of w is square root of 2.
01:54
So 4 multiplied by 3, which is the length of b.
01:58
So 12.
02:02
Okay, 12 plus 2.
02:04
So we got 12 plus 11 which is 23 okay now we solved a and we just need to find the projection of u so i'm just going to write these two vectors here u is negative 153 so negative 153 and v and v is negative 1 1 negative 3 okay, let's check if they are the right ones...