00:01
We want to find the length of op in figure 14.
00:06
Now notice that op is this vector right here from the origin to p.
00:20
And it looks like all we did to get this was project down u onto v.
00:29
So this is really the projection of u onto v, which recall is the equation u.
00:43
Dot v over the magnitude of v squared times b.
00:51
Now, to get the magnitude, or to get the length of this vector, we would just take the magnitude of the projection.
01:04
And in doing this, recall one of the properties of magnitude is we can pull out scalers or just constants.
01:17
So we'd have u .d.
01:19
B over the magnitude of v squared, and we would just have left the magnitude of b.
01:25
But notice that we have a magnitude of v squared in the denominator there.
01:30
So we would end up with u dotted with b over the magnitude of v.
01:36
So we've significantly lessened our workload since all we need to do is find the length that we actually don't want that vector.
01:47
So off on the slide, let's calculate each.
01:51
So u .v is going to be, so we have 3, 5 dotted with 8, 2, and now we would just multiply these component -wise, so we'd get 3 times 8 plus 5 times 2...
