# 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>?

Nov 16, 2016

The vector is =〈4,12,16〉

#### Explanation:

The cross product is calculated by the determinant

$\vec{u} . \vec{v} =$

〈1,-3,2〉x〈5,1,-2〉

∣ ((i,j,k) , (1,-3,2) , (5,1,-2)) ∣

$= i \left(6 - 2\right) - j \left(- 2 - 10\right) + k \left(1 + 15\right)$

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 $\vec{w}$ is perpendicular to $\vec{u}$ and $\vec{v}$