to #1:

Therefore a vector which has the same direction as and has the magnitude 3 has the components:

to #2:

And therefore you have to solve for x:

(since only the positive value should be used). That means:

to #3:

Let . Let

Then you know:

and therefore the vector

is perpendicular to

Actually this is the equation of a plane passing through the origin with as it's normal vector.

Choose numbers for r and s to build vectors and do the required examinations.