This week we focused more on lessons in class and less on alex. We are finally get back into trig and preparing for our trig exam. Next week our blue pie for alex will be due so we can get into logs and more things with trig. In the section below I will explain our notes on 3D. Chapter 12 has been a lot of formulas and has been pretty simple if you study.

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