Question

What is the cross product of `[-2,0,3]` and `[1,-1,3]`?

Answer 1

The vector is `=〈3,9,2〉`

Explanation:

The cross product of 2 vectors is given by the determinant.

`| (hati,hatj,hatk), (d,e,f), (g,h,i) |`

Where, `〈d,e,f〉` and `〈g,h,i〉` are the 2 vectors.

So, we have,

`| (hati,hatj,hatk), (-2,0,3), (1,-1,3) |`

`=hati | (0,3), (-1,3) |-hatj | (-2,3), (1,3) |+hatk | (-2,0), (1,-1) |`

`=hati(3)+hatj(9)+hatk(2)`

So the vector is `〈3,9,2〉`

To verify, we must do the dot products

`〈3,9,2〉.〈-2,0,3〉=-6+0+6=0`

`〈3,9,2〉.〈1,-1,3〉=3-9+6=0`