Distance in Space

There is also a distance formula for points in space. If A has coordinates (a,b,c) and D has coordinates (d,e,f) then the distance from A to D is  

$$\sqrt{(a-d)^2 + (b-e)^2 + (c-f)^2}.$$ (2)

Exercises:

1.

Find the distance between each pair of points:

(a)

(2,3,4) and (5,-3,5);

(b)

(6,-3,2) and $(4,\pi,1/8)$;

(c)

(-1,2,-3) and (99,4,-9).

2.

Describe geometrically the solution to the inequality
$\sqrt{(x-1)^2 + (y-2)^2 + (z-3)^2} < 12$.