# What is the cross product of <5 , 5 ,-7 > and <5 ,6 ,-3 >?

Oct 29, 2016

$< 27 , - 20 , 5 >$

#### Explanation:

Convert to $\hat{i} , \hat{j} , \hat{k}$ notation

$\overline{A} = 5 \hat{i} + 5 \hat{j} - 7 \hat{k}$
$\overline{B} = 5 \hat{i} + 6 \hat{j} - 3 \hat{k}$

The cross product can be computed using a determinant:

barA xx barB = | (hati, hatj, hatk, hati, hatj), (5, 5, - 7,5, 5), (5, 6, -3, 5, 6) | =

$\left\{\left(5\right) \left(- 3\right) - \left(- 7\right) \left(6\right)\right\} \hat{i} + \left\{\left(- 7\right) \left(5\right) - \left(5\right) \left(- 3\right)\right\} \hat{j} + \left\{\left(5\right) \left(6\right) - \left(5\right) \left(5\right)\right\} \hat{k} =$

$27 \hat{i} - 20 \hat{j} + 5 \hat{k}$