# What is the cross product of (- 5 i + 4 j - 5 k) and (i + j -7k)?

Jul 3, 2016

$= - 23 \hat{i} - 40 \hat{j} - 9 \hat{k}$

#### Explanation:

the cross product is the determinant of this matrix

$\left[\begin{matrix}\hat{i} & \hat{j} & \hat{k} \\ - 5 & 4 & - 5 \\ 1 & 1 & - 7\end{matrix}\right]$

which is

$\hat{i} \left[\left(4\right) \left(- 7\right) - \left(1\right) \left(- 5\right)\right]$

$- \hat{j} \left[\left(- 5\right) \left(- 7\right) - \left(1\right) \left(- 5\right)\right]$

$+ \hat{k} \left[\left(- 5\right) \left(1\right) - \left(1\right) \left(4\right)\right]$

$= \left[\begin{matrix}- 23 \\ - 40 \\ - 9\end{matrix}\right]$