00:01
On this question, we have a vector v, which is the vector negative 4 -22, and we're going to calculate v -cross -i, v -cross -j, and v -cross -k.
00:10
Well, let's see.
00:11
Let's do v -cross -i to begin.
00:15
So to compute this cross -product, we put i, j, k across the top row, negative 4, 2, 2 across the middle row, and then remember what i is.
00:32
I is the vector 1 -0 -0.
00:36
So 1 -0 across the bottom row.
00:42
And so what do we get? we get i times 0 minus 0.
00:51
And then it's minus j times 0 minus 2.
01:00
Negative 4 times 0 minus 1 times 2.
01:05
And then it's plus k times negative 4 times 0 minus 1 times 2 is 2.
01:16
We are getting the vector 0 2 negative 2.
01:23
0 2 negative 2.
01:28
Now let's take v cross j.
01:33
Remember what j is.
01:35
J is the vector 0 1, 0.
01:41
So across the top row, i, j, k.
01:46
Across the middle row, negative 4, 2, 2, and across the bottom row, 0, 1 ,0...