# How do you find the cross product and verify that the resulting vectors are perpendicular to the given vectors <4,0,=2>times<-7,1,0>?

Oct 23, 2016

The vector is 〈2,14,4〉

#### Explanation:

The cross product of 〈4,0,-2〉xx〈-7,1,0〉 is

$\vec{i}$$\textcolor{w h i t e}{a a}$$\vec{j}$$\textcolor{w h i t e}{a a}$$\vec{k}$
$4$$\textcolor{w h i t e}{a a a}$$0$$\textcolor{w h i t e}{a a}$$- 2$
$- 7$$\textcolor{w h i t e}{a a}$$1$$\textcolor{w h i t e}{a a a}$$0$

cross product $=$$\left(\vec{i} \left(0 + 2\right) + \vec{j} \left(- \left(0 - 14\right)\right) + \vec{k} \left(4 - 0\right)\right)$

=〈2,14,4〉
To check this we do the dot products

〈2,14,4〉.〈4,0,-2〉$= 8 + 0 - 8 = 0$

〈2,14,4〉〈-7,1,0〉$= - 14 + 14 + 0 = 0$

As the dot products are $= 0$
So the 3 vectors are perpendicular