1. ## Vector stuff

Find an equation of the set of all points equidistant from the points A (-5, 6, 3) and B (3, 4, -8).

I didn't really know what to do on the first one. I took the midpoint of those two points to get the center = (-1, 5, -2.5). I then used the distance formula between the points A and B to get the diameter, then divided by 2 and squared and set it equal to the equation of the center. I also tried using the distance formula between what I got as the center and point A, which is the radius, and squaring it. It said both were wrong, which I figured, so I now don't know what to do.

Find the volume of the solid that lies inside both of the spheres:
x^2 + 18x + y^2 - 12y + z^2 + 40 = 0
x^2 + y^2 + z^2 = 81

For the second one, I completed the square for the first equation to get: (x+9)^2 + (y-6)^2 + (z+2)^2 = 81, the center is (-9, 6, -2) with R=9
x^2 + y^2 + z^2 = 81, the center is (0, 0, 0) with R=9
That's where I'm stuck at.

These are the last two from my homework exercises. There aren't any examples in the book like these so there isn't anything for me to follow.

2. The part (a) is a plane containing (-1,5,-2.5) and perpendicular to $\displaystyle \vec{AB}$.

3. I don't know what to do with that. I know it's a plane, as the squared variables should drop, but I don't even know where to begin.

Any help on the other problem from anyone? I'd greatly appreciate it. These are due by 11:30 tonight.