# What is the cross product of (2i -3j + 4k) and (- 5 i + 4 j - 5 k)?

I found: $- i - 10 j - 7 k$
Calling the two vectors $\vec{u} \mathmr{and} \vec{v}$ we can use the definition of Cross Product to get:
$\vec{u} \times \vec{v} = | \left(i , j , k\right) , \left({u}_{x} , {u}_{y} , {u}_{z}\right) , \left({v}_{x} , {v}_{y} , {v}_{z}\right) | = | \left(i , j , k\right) , \left(2 , - 3 , 4\right) , \left(- 5 , 4 , - 5\right) | =$ evaluating the Determinant:
$\vec{u} \times \vec{v} = = - i - 10 j - 7 k$