Question

What is the cross product of `<-3,0,1>` and `<3,-6,4>`?

Answer 1

`[6, 15, 18]`

Explanation:

The cross product of two vectors is also a vector. If vector `veca = [a1, a2, a3]` and vector `vecb = [b1, b2, b3]` then the components of the cross product vector `vecv = vecaxxvecb` can be calculated from

`v_1 = a_2b_3 - a_3b_2`
`v_2 = a_3b_1 - a_1b_3`
`v_3 = a_1b_2 - a_2b_1`

The best way to memorise these terms is to express the two vectors as a determinant and study the pattern of math operations that will yield the same vector components. If want to compute vector products really fast then you will need to write a short computer program or punch in the formulas in a Spreadsheet.