Question

What is the cross product of `<4 , 5 ,-9 >` and `<4, 8 ,-2 >`?

Answer 1

The answer is `=〈62,-28,12〉`

Explanation:

The cross product of 2 vectors, `〈a,b,c〉` and `d,e,f〉`

is given by the determinant

`| (hati,hatj,hatk), (a,b,c), (d,e,f) |`

`= hati| (b,c), (e,f) | - hatj| (a,c), (d,f) |+hatk | (a,b), (d,e) |`

and `| (a,b), (c,d) |=ad-bc`

Here, the 2 vectors are `〈4,5,-9〉` and `〈4,8,-2〉`

And the cross product is

`| (hati,hatj,hatk), (4,5,-9), (4,8,-2) |`

`=hati| (5,-9), (8,-2) | - hatj| (4,-9), (4,-2) |+hatk | (4,5), (4,8) |`

`=hati(-10+72)-hati(-8+36)+hatk(32-20)`

`=〈62,-28,12〉`

Verification, by doing the dot product

`〈62,-28,12〉.〈4,5,-9〉=248-140-108=0`

`〈62,-28,12〉.〈4,8,-2〉=248-224-24=0`

Therefore, the vector is perpendicular to the other 2 vectors