00:01
So for number 10, we want to take the dot product of a and b and set it equal to 0, because when the dot product is equal to 0, your two vectors are orthogonal.
00:13
So we're going to take 5, negative 4, comma 3, and dot that with negative 2, comma 3, comma k, and set it equal to 0.
00:22
So we get 5 times negative 2 plus negative 4 times 3 plus 3k equals 0.
00:31
So we get negative 10 minus 12 plus 3k equals 0.
00:38
And when we solve for 3k, we get 3k equals 22.
00:43
So then k is going to equal 22 divided by 3.
00:48
All right, so what we need to do is find the cross product between a and b, and then multiply that, or not multiply, take the dot product of that by c.
00:59
Okay, so this is what the cross product between a and b looks like in the determinant form.
01:05
So to find the i component, we're going to find the determinant by crossing out the row and column that includes i.
01:13
So the determinant is going to be negative 2, 2, 4, negative 3.
01:19
We repeat the same thing for the j.
01:22
So we're going to cross out the row and column that include j, but now we have to subtract the determinant.
01:28
So 5, 0, 4, negative 3.
01:32
And then lastly, we want to find the k component.
01:35
So we cross out the row and column that include k, and we're going to add the determinant 5, 0, negative 2, 2.
01:44
So for the i component, that's going to be negative 2 times negative 3.
01:51
And we're going to subtract 2 times 4.
01:55
Then for the j, we're going to have negative of 5 times negative 3 minus 0 times 4.
02:07
And for k, we're going to have 5 times 2 minus 0 times negative 2...