# Urgent: Three-dimensional space/vectors problems

• Feb 6th 2008, 07:56 PM
Fooldj
Urgent: Three-dimensional space/vectors problems
Hi, i'm taking calculus 3 for honors credit. I'm trying to complete these last few problems, but i can't seem to figure them out, or find anything on google. Maybe i'm too tired or something, but any help would be grateful.

#1 The two spheres x^2 + y^2 + z^2 + 4x - 2y + 4z +5 = 0 and x^2 + y^2 + z^2 = 4 overlap. What is the volume of the solid that lies inside both?

#2 If r=<x,y,z>, a = <a1,a2,a3> and b = <b1,b2,b3, then the vector equation (r-a)(r-b) = 0 represents a sphere. Find it's center and radius.

#3 Take a box (cubical) with side length 1 meter. Pack in nine spherical balls, each of radius r. Things should be tight: The center of one ball should be at the center of the cube, and it should touch the other eight balls. Each of these other eight balls should touch three sides of the box. Find r.
• Feb 7th 2008, 05:11 AM
Fooldj
for the second problem i think i figured out how to get the radius. The vector equation is saying that the two vectors (r - a) and (r - b) are perpendicular to each other. If a right triangle is in a sphere, then the hypotnuse is the diameter of the sphere. So i got the magnitude of (r - a) and (r - b), then used pythagorean theorem to get the diameter, just divide by 2 and you have the radius. No clue how to get the center though. (sorry for poor spelling, been up for over 36 hours now)