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.