Calculus cross product

Question

Let a=<−5,3,1> and b=<5,1,−5>. Find a x b

Answer 1

Setup a basic matrix like the one above. The cross product will yield a vector, so it'll have i, j, and k components.

To determine the i component, cover the row and column containing i in the matrix. All that will remain is the matrix

Compute the determinant of this matrix (3*(-5) - 1*1 = -16) and you'll find the i component (-16i).

To determine the j component, cover the row and column containing j in the matrix and compute the determinant of the resultant matrix. You should get (-5*(-5) - 1*5 = 20). NEGATE this and you will have the j component (-20j).

To determine the k component, cover the row and column containing k in the matrix and compute the determinant of the resultant matrix. You should get (-5*1 - 3*5 = -20). Then, the k component is -20k.

Putting them together, we have that a x b = <-16, -20, -20>.