$(\lambda\hat{i} + 2\hat{j} - \hat{k}) \times (\hat{i} - \hat{j} + \hat{k}) = \hat{i} - 3\hat{j} + \mu\hat{k}$. What is $\lambda + \mu$?

Explanation

1. 01

   $\hat{i}(2 \cdot 1 - (-1)(-1)) - \hat{j}(\lambda \cdot 1 - (-1) \cdot 1) + \hat{k}(\lambda(-1) - 2 \cdot 1) = \hat{i} - (\lambda + 1)\hat{j} - (\lambda + 2)\hat{k}$.

2. 02

   Matching: $\lambda + 1 = 3$, so $\lambda = 2$, and $\mu = -(\lambda + 2) = -4$: $\lambda + \mu = -2$.