00:01
We're being asked to find the vector that is orthogonal to the two given vectors, which i'm going to call vnw.
00:05
Well, remember, to find a vector that's orthogonal to two vectors, we have to find the cross product because the cross product will result in a vector.
00:13
So in this case, we're going to find the cross product of v and w.
00:16
So to do this, we're going to have our standard vectors.
00:18
And remember, we always use matrices to do this.
00:21
So in our first row, we're going to have i, j, and k, our standard vectors.
00:25
In our second row, i'm going to have our components for our vector v, which would be 5, 9 ,000, negative 2 and 1.
00:31
And our last row will be the components of w, which are 1, 0, and negative 3.
00:36
So now we just have to find the determinant.
00:39
So the best way to think about this is our first one is going to be i, and then we have to find the determinant and you cross off the column i is in and the rows i is in.
00:47
So it would be the determinant of negative 2, 1, 0, and negative 3.
00:53
Then if i get rid of that, actually i'll do this in red here.
00:57
For our next one, we're going to do the opposite for j.
01:00
So here we're crossing off j and i'm going to do this lightly, cross off the row that j's in as well.
01:09
So that will leave us with 5 -1 -1 and negative 3.
01:13
Then for our last one, which i'm going to put underneath here, because i'm running out of room, we're going to add our standard vector for k.
01:19
So i'm going to cross off the column k's in as well as its row, which leaves us with 5, negative 2, 1, and 0.
01:26
So now we're going to put this all together.
01:28
So i'm going to slide this over here...
