3-D
The formula to find midpoint is (x1+x2/2, y1+y2/2, z1+z2/2)
IABI = square root (x2-x1)squared +(y2-y1)squared + (z2-z1)squared
Vector equation = (x, y, z) = (xo, yo, zo) + t(a, b, c) *a, b, and c is your vector

EXAMPLE 1: A sphere has points (6, 2, 3) and (2, 2, 7). Find the center and radius.
A). Use the midpoint formula first.
(6+2/2, 2+2/2, 3+7/2) = (4, 2, 5)
B). Now use the IABI formula.
Square root (2-6)squared + (2-2)squared + (7-3)squared = 0
C). The answer you get there is your diameter.
D. Now plug the answer you got from step A into the vector equation formula.
(x-4)squared + (y-2)squared + (z-5)squared = 0 (radius squared)

EXAMPE 2: Find the vector and parametric equations of the line containing (1, 3, 5) and (2, 8, 9)
A). Use your vector equation formula.
(x, y, z) = (1, 3, 5) + t(1, 5, 4)
*(1, 5, 4) is found by subtracting x2-x1, y2-y1, and z2-z1
B). x = 1 + t, y = 3 + 5t, and z = 5 + 4t


Alrighttttttttttttttt, hope everyone has a great weekend and good luck to everyone at Carnival Ball :)