Question

What is the cross product of `<5 , 5 ,-7 >` and `<5 ,6 ,-3 >`?

Answer 1

`<27, -20, 5>`

Explanation:

Convert to `hati, hatj, hatk` notation

`barA = 5hati + 5hatj - 7hatk`
`barB = 5hati + 6hatj - 3hatk`

The cross product can be computed using a determinant:

#barA xx barB = | (hati, hatj, hatk, hati, hatj), (5, 5, - 7,5, 5), (5, 6, -3, 5, 6) | = #

`{(5)(-3)-(-7)(6)}hati + {(-7)(5) - (5)(-3)}hatj + {(5)(6) - (5)(5)}hatk =`

`27hati - 20hatj + 5hatk`