# What is the cross product of [-2,0,3] and [1,-1,3] ?

Nov 20, 2016

The vector is =〈3,9,2〉

#### Explanation:

The cross product of 2 vectors is given by the determinant.

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

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

So, we have,

$| \left(\hat{i} , \hat{j} , \hat{k}\right) , \left(- 2 , 0 , 3\right) , \left(1 , - 1 , 3\right) |$

$= \hat{i} | \left(0 , 3\right) , \left(- 1 , 3\right) | - \hat{j} | \left(- 2 , 3\right) , \left(1 , 3\right) | + \hat{k} | \left(- 2 , 0\right) , \left(1 , - 1\right) |$

$= \hat{i} \left(3\right) + \hat{j} \left(9\right) + \hat{k} \left(2\right)$

So the vector is 〈3,9,2〉

To verify, we must do the dot products

〈3,9,2〉.〈-2,0,3〉=-6+0+6=0

〈3,9,2〉.〈1,-1,3〉=3-9+6=0