# What is the cross product of [2,4,5] and [0,1,2] ?

Oct 28, 2016

The cross product is 〈3,-4,2〉

#### 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 〈2,4,5〉 and 〈0,1,2〉 is 〈3,-4,2〉

Verification by making the dot product
〈2,4,5〉.〈3,-4,2〉=6-16+10=0
and 〈0,1,2〉.〈3,-4,2〉=0-4+4=0

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