Question

What is the cross product of `[1,-1,3]` and `[5,1,-3]`?

Answer 1

`(0, 18, 6)`

Explanation:

The easiest way to write out the cross product is as a determinant. This can be written as
`(1,-1,3) times (5,1,-3) = |(hati,hatj,hatk),(1,-1,3),(5,1,-3) |`

Calculating this,

`= hati(-1* -3 - 1 * 3) - hatj(1*-3-5*3) + hatk(1*1 - 5 * -1)`
`= - hatj(-3-15) + hatk(1 + 5) = 18hatj + 6hatk = (0,18,6)`