Exercise 19

Let $\vx = \langle 1, 1, 1 \rangle$ and $\vy = \langle 0, 3, -2 \rangle$.

1. Are $\vx$ and $\vy$ orthogonal? Are $\vx$ and $\vy$ parallel? Clearly explain how you know, using appropriate vector products.

2. Find a unit vector that is orthogonal to both $\vx$ and $\vy$.

3. Express $\vy$ as the sum of two vectors: one parallel to $\vx$, the other orthogonal to $\vx$.

4. Determine the area of the parallelogram formed by $\vx$ and $\vy$.