Help with some homework problems

Hey, I have a few problems in my calc 3 night course that I'm having some trouble with, with this material in particular. These are from an older homework I need to work through again so an outline of the necessary procedure would really help. Any solutions or help guides would be greatly appreciated.

1. Find the point S such that the vertices P, Q, R and S form a parallelogram with Q and R adjecent to P if P=(3,-5,2), Q=(8,0,-2) and R=(-6,2,-1)

2.find the volume of a parallelepiped that has u, v and w as adjacent edges, if u=(2,-1,7), v=(0,3,35) and w= (0,-6,10)

3. Find the distance from point P(11,5,-3) to the line through A(3,-4,5) and B(10,-11,11)

4. find two unit vectors that are perpendicular to both u and v if u=(9,9,-6) and v=(-4,5,1)

Thanks again, I find this material much more difficult to grasp on a more complex level than the later stuff.

Re: Help with some homework problems

Have you attempted any of the solutions?

If so, can you show us any of your working?

Hint for Q1:

Parallelogram law (Use 'P' as the anchor point and make two direction vectors).

Hint for Q2:

Volume is the triple cross product: $\displaystyle \mathbf{u} \;\cdot \; (\mathbf{v}\times \mathbf{w}) $

I'll gladly post hints for the other two when you've shown some working for them. :)

Re: Help with some homework problems

I certainly will but I'm going to.need a few days, I have several newer homework assignments to finish and it's been so long , in the course since I've done that I'm going to have to go back and look a bunch of stuff up again. Once I get stared I'll show all my work though. I posted them here soI'd have some idea of what needed to be done when I got to them.