For a given plane and vectors, and vectors answer yes or no to the following questions

Question

Given the plane is $2x+y-2z=-2$ and the vectors $u=\frac{1}{3}(2,-2,1)$ and $v=\frac{1}{3}(1,2,2)$, answer the following questions.

1. Find $u \times v$

2. Are $u$ and $v$ orthogonal?

3. Is $u$ a unit vector?

4. Is $v$ a unit vector?

5. Is $u$ parallel to the plane?

6. Is $v$ parallel to the plane?

Answer 1

Hint. Note that the vector $w=(2,1,-2)$ is orthogonal to the plane $2x+y-2z=-2$. Therefore a vector is parallel to the plane iff it is orthogonal to $w$.