Thursday, April 10, 2014

11.1-the three dimensional coordinate system

X= distance from yz-plane to P
Y=distance from xz-plane to P
Z=distance from xy-plane to P
Distant formula
D=[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]^1/2

Let's say we had to find the distance between (2,1,3) and (-1,2,1)
D= [(-1 - 2)^2 + (2 - 1)^2 + (1 - 3)^2]^1/2
  = [ 9 + 1 + 4]^1/2
  = (14)^1/2

Midpoint 
((X1 + x2))/2, ((y1 + y2))/2, ((z1 + z2))/2

Let's say we had to find the midpoint between (5,-2,3) and (0,4,4)
(5+0)/2, (-2+4)/2, (3+4)/2) = (5/2,1,7/2)

Standard equation of a sphere
[(x-h)^2 + (y-k)^2 + (z-j)^2] = r^2

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