Exercise 18

Let $\vu = 2\vi + \vj$ and $\vv = \vi + 2\vj$ be vectors in $\R^3$.

1. Without doing any computations, find a unit vector that is orthogonal to both $\vu$ and $\vv$. What does this tell you about the formula for $\vu \times \vv$?

2. Using the properties of the cross product and what you know about cross products involving the fundamental vectors $\vi$ and $\vj$, compute $\vu \times \vv$.

3. Next, use the determinant version of Equation this equation to compute $\vu \times \vv$. Write one sentence that compares your results in (a), (b), and (c).

4. Find the area of the parallelogram determined by $\vu$ and $\vv$.