Cross products in action - an example involving 3x3 determinants. Compute the cross product, u v, of the following two vectors: u = < 3, 1, 0 >, v = < 5, 2, 1> But computing the value of what is called the determinant of a matrix , can be tricky. We"ll leave the theory for another course, but for a 3x3 matrix, there there are two common methods: Copy the first two columns to the right of the matrix. Compute the product along the diagonal, down to the right, and add. Compute the products along the diagonal, down and to the left, and subtract. i. 1 5 2 (1)( 1) i (0)(5) j (3)2 k (1)5 k (0)(2) i (3)( 1) j ( 1 0) i (0 3) j (6 5) k. Write each of the 2x2 minors corresponding to i, j and k. Compute the value of each minor. (call them m11, m12, m13 respectively. )
