1. The problem statement, all variables and given/known data

Question

Find the vector product of Vector A cross Vector B(expressed in unit vectors) of the two vectors. What is the magnitude of the vector product?

2. Relevant equations
Vector A= 5.00i + 2.00j
Vector B= 3.00i - 1.00j

3. The attempt at a solution

I know how to get the dot product of the two, but how do I find the cross product??

Answer 1

The cross product is the determinant of a 3x3 matrix formed by the unit vectors i, j, k, A, and B. (Break A and B into x, y, and z components).

i j k
5 2 0
3 -1 0

The result is a vector orthogonal to both A and B; because A and B do not have z components, the result should be something like 0i + 0j + Ck, where C is a scalar.