Chapter 11.4, Problem 1ES

(a) Use a determinant to find the cross product $\text{i}\times \left(\text{i}+\text{j}+\text{k}\right)$

(b) Check your answer in part (a) by rewriting the cross product as $\text{i}\times \left(\text{i}+\text{j}+\text{k}\right)=\left(\text{i}\times \text{i}\right)+\left(\text{i}\times \text{j}\right)+\left(\text{i}\times \text{k}\right)$ and evaluating each term.