# What is the cross product of [0,8,5] and [1, 4, -2] ?

Apr 3, 2017

#### Answer:

The vector is =〈-36,5,-8〉

#### Explanation:

The cross product is a vector perpendiculat to 2 other vectors

$| \left(\vec{i} , \vec{j} , \vec{k}\right) , \left(d , e , f\right) , \left(g , h , i\right) |$

where 〈d,e,f〉 and 〈g,h,i〉 are the 2 vectors

Here, we have veca=〈0,8,5〉 and vecb=〈1,4,-2〉

Therefore,

$| \left(\vec{i} , \vec{j} , \vec{k}\right) , \left(0 , 8 , 5\right) , \left(1 , 4 , - 2\right) |$

$= \vec{i} | \left(8 , 5\right) , \left(4 , - 2\right) | - \vec{j} | \left(0 , 5\right) , \left(1 , - 2\right) | + \vec{k} | \left(0 , 8\right) , \left(1 , 4\right) |$

$= \vec{i} \left(- 2 \cdot 8 - 5 \cdot 4\right) - \vec{j} \left(- 2 \cdot 0 - 5 \cdot 1\right) + \vec{k} \left(0 \cdot 4 - 8 \cdot 1\right)$

=〈-36,5,-8〉=vecc

Verification by doing 2 dot products

〈-36,5,-8〉.〈0,8,5〉=-36*0+5*8-5*8=0

〈-36,5,-8〉.〈1,4,-2〉=-36*1+5*4+2*8=0

So,

$\vec{c}$ is perpendicular to $\vec{a}$ and $\vec{b}$