Question

How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors `<1,-3,2>times<5,1,-2>`?

Answer 1

The vector is `=〈4,12,16〉`

Explanation:

The cross product is calculated by the determinant

`vecu.vecv=`

`〈1,-3,2〉`x`〈5,1,-2〉`

`∣ ((i,j,k) , (1,-3,2) , (5,1,-2)) ∣`

`=i(6-2)-j(-2-10)+k(1+15)`

`vecw=〈4,12,16〉`

To verify, we do the dot products

`〈4,12,16〉.〈1,-3,2〉=4-36+32=0`

`〈4,12,16〉.〈5,1,-2〉=20+12-32=0`

Therefore `vecw` is perpendicular to `vecu` and `vecv`