# 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>?

Oct 28, 2016

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

$\vec{u}$x$\vec{v}$ =〈u_2v_3-u_3v_2,u_3v_1-u_1v_3,u_1v_2-u_2v_1〉
This vector is perpendicular to $\vec{u}$ and $\vec{v}$

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