This week we learned a few new sections, had to complete a total of 70 modules on aleks, and took our Chapter 12 test. The next week our whole blue pie will have to be complete. In the section below I will explain our notes on 3D. This Chapter is mostly formulas and is pretty easy to remember if you study it.

Formulas you need to know for this section are below:

AB = square root (x2-x1)2 + (y2-y1)2 + (z2+z1)2

Midpoint = (x1 + x2/2) (y1 + y2/2) (z1 + z2/2)

Equation of a Sphere = (x-xo)2 + (y-yo)2 + (z-zo)2 = r2

Vector equation (x,y,z) = (xo, yo, zo) + t(a,b,c)

Vector addition, magnitude, dot product, etc.are just a little different but follow the same formulas as earlier sections. They just have an extra variable in the formula unlike before.

Example

Find the center and radius Point A (8,4,2) Point B (2, 8,6)

Center – 9 + 7/2 = 8, 5 + 3/2 = 4, 7 + 5/2 = 6 (8,4,6)

Radius – square root (7 - 9)2 + (3 - 5)2 + (5 – 7)2 = 6+ 6 + 6= square root 16/2 = square root 8

Find the equation
(x – 8)2 + (y – 4)2 + (z – 6)2 = 8