Question

How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors `<5,2,3>times<-2,5,0>`?

Answer 1

The cross product is `〈-15,-6,29〉`

Explanation:

The cross product of 2 vectors `vecu=〈u_1,u_2,u_3〉` and `vecv=〈v_1,v_2,v_3〉` is given by

`vecu`x`vecv` `=〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉`
This vector is perpendicular to `vecu` and `vecv`

So the cross product of `〈5,2,3〉` and `〈-2,5,0〉` is `〈-15,-6,29〉`

Verification by making the dot product
`〈5,2,3〉.〈-15,-6,29〉=-75-12+87=0`
and `〈-2,5,0〉.〈-15,-6,29〉=30-30+0=0`

As both dot products are `=0` so the vector is perpendicular to the other 2 vectors