Ok so this week has been kind of a blur. For some reason I can’t remember exactly what we did this week except I know we learned a couple of new sections. One of these sections has something about 3D. I can’t even remember the section number but anyway it has something to do with vectors and midpoint equations. Here are the notes Mrs. Robinson gave us.

|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. all follow the same formula with extra variable.

Example

Find the center and radius Point A (9,5,7) Point B (7, 3,5)

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 = 4 + 4 + 4 = square root 12/2 = square root 3

Find the equation
(x – 8)2 + (y – 4)2 + (z – 6)2 = 3