## Problem on computing a cross product

Compute $\bfi \times (\bfi + \bfk)$ in two ways:
1. By the determinant formula
2. By expanding the sum and recalling the cross products of standard coordinate vectors with each other
• ## Solution

#### Part (a)

Recall that:
We identify $\bfx = \bfi = \langle 1, 0, 0 \rangle$ and $\bfy = \bfi + \bfk = \langle 1, 0, 1 \rangle.$
Hence,

#### Part (b)

Recall that
Hence, $\bfi \times (\bfi + \bfk) = \bfi \times \bfi + \bfi \times \bfk$.
Recall that
Hence, $\bfi \times \bfi = 0$, and $$\bfi \times (\bfi + \bfk) = -\bfj.$$