Exercise 17

Let $\vv = \langle -2, 5 \rangle$ in $\R^2$, and let $\vy = \langle 0, 3, -2 \rangle$ in $\R^3$.

1. Is $\langle 2, -1 \rangle$ perpendicular to $\vv$? Why or why not?

2. Find a unit vector $\vu$ in $\R^2$ such that $\vu$ is perpendicular to $\vv$. How many such vectors are there? Justify your answers.

3. Is $\langle 2, -1, -2 \rangle$ perpendicular to $\vy$? Why or why not?

4. Find a unit vector $\vw$ in $\R^3$ such that $\vw$ is perpendicular to $\vy$. How many such vectors are there?Justify your answers.

5. Let $\vz = \langle 2, 1, 0 \rangle$. Find a unit vector $\vr$ in $\R^3$ such that $\vr$ is perpendicular to both $\vy$ and $\vz$. How many such vectors are there? Explain your process.