00:01
All right, so let's write the qp vector and qr vector, and then we're going to use dot product to find the angle between them.
00:07
Okay, qp is p minus q, so 7, 0 minus 8 is negative 8, and then 4 minus 4 is 0.
00:18
And then qr is qr vector is r minus q, which is 7, 8 minus 8, 0 minus 8, 0 minus 4 is negative 4.
00:34
Also, we need the magnitude of qp and magnitude of qr.
00:41
Magnitude of qp is 7 square is 49 plus 64.
00:47
And then this one is 49 plus 16.
00:52
So this is 5965 and this one is 109 -130.
01:01
Okay, so then qp dot qp.
01:06
Qr is equal to magnitude of qp, magnitude of qr, and cosine of the angle.
01:18
Angle is the angle we're looking for...