00:01
In this problem, we are going to use the concept of cross products of vectors in order to determine the area of a parallelogram.
00:08
Now in this problem, the given vectors are the vectors u, which is 3 minus 1, 4, and the vector v, which is given to be 6 minus 2, 8.
00:21
Now the area of the parallelogram determined by these two vectors is equal to the modulus of the cross product, u cross v.
00:29
So first of all, we need to find the cross product u cross b.
00:33
Now, in order to do that, first of all, we write a matrix.
00:36
The first row being the components of the vector u, and the second row being the components of the vector v.
00:43
Now, we use this matrix in order to determine the cross product.
00:50
Now, the first component of the cross product will be the determinant of the numbers left over on deleting the first column of the matrix.
00:57
So this will be the determinant minus 1, 4.
01:00
Minus 2, 8.
01:02
Now the second component will be the negative of the determinant of the numbers left on deleting the second column of the matrix.
01:09
So this will be 3, 4, 6, 8.
01:13
And the last component will be the determinant of the numbers left on deleting the third column of the matrix...