00:02
Hi there, so for this problem, we are given these three vectors.
00:06
And for part a of this problem, what we are asked to do is to determine which two vectors form a right angle triangle.
00:16
We know that two vectors form a right angle triangle when they form an angle of 90 degrees.
00:25
Now this means that the dot product between those two vectors should be equal to zero.
00:30
So what we are going to do is to dot the dot product between two vectors in here, and that will be equal to zero.
00:40
For example, we can try to do the dot product between the vector u and the vector b.
00:47
When we do that, remember that the dot product is a number, and it is just a sum of the product between component by component.
00:56
So for example, in this case, it's two times zero, so that will be zero times two plus, then we will have one times two.
01:11
And finally, we have one times zero, so that will give us zero, okay? so from this, we obtain two.
01:19
Now this value is different than zero, so these two vectors cannot form a right angle triangle.
01:27
Now let's do now the vector b with dot product with the vector w.
01:32
So in this case, as you can see, we will have then two times minus one, so that will give us minus two.
01:42
Then this plus two times one, so that will give us two, and zero times zero, which give us zero.
01:50
Minus two plus two give us zero, so then we can answer that the two vectors that form a right triangle is the vector b with the vector w.
02:04
So that's the solution for part a of this problem.
02:11
Now for part b, we are asked to determine the angle between the vector u and the vector w...