Three-Dimensional Coordinate Systems: Examples

1. Find the distance between the points (-1,3,-5) and (4,-5,1).

Anwser:

>	sqrt((4-(-1))^2+(-5-3)^2+(1-(-5))^2);

2. Find the equation of a sphere with a center of (1,-2,-3) and a radius of 4.

Anwser

>	(x-1)^2+(y+2)^2+(z+3)^2=16;

Extra: How to Graph the Sphere

First solve for z:

>	solve((x-1)^2+(y+2)^2+(z+3)^2=16,z);

>	plot3d([-3+(11-x^2+2*x-y^2-4*y)^(1/2), -3-(11-x^2+2*x-y^2-4*y)^(1/2)], x=-5..5, y=-5..5)

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