00:01
In this problem, we are given two vectors and told that they create a parallelogram and asked to find the area of that parallelogram.
00:11
Our first step is going to be to rewrite the vectors into the normal vector form we are used to, which is going to be for u1, negative 1 ,1, taking the coefficients of ij and k, and for v, it's going to be 1, 1, negative 1.
00:31
Now we are going to take the cross product of those two vectors.
00:35
So we're going to take u cross v.
00:40
And our first step in that is going to be to write a matrix with its first row as i, j, and k, its second row as the components of u, which are 1, negative 1, and 1.
00:54
And its third row is the components of v, which are 1, 1, negative 1.
00:59
Now, to get i's component, we're going to cross out the first column and take the determinant of this 2x2 matrix, which is going to be negative 1 times negative 1 minus 1 times 1, which is going to be 1 minus 1, that's 0.
01:17
We subtract j's component, and then we cross out the middle column, take the determinant of this 2x2 matrix.
01:27
We get 1 times negative 1 minus 1, or negative 1, minus 1, that is negative 2...