Dot Product and Distance (2D, 3D, ...)
a.k.a. Scalar Product
/ x1 / x2
u.v = | y1 . | y2 = x1.x2 + y1.y2 + z1.z2
\ z1 \ z2
Distance between M and P :
u = MP
Dist (M,P) = ||u|| = SquareRoot(u.u) = SquareRoot( (a2-a1)2
+ (b2-b1)2 + (c2-c1)2 )
v = 0 <=> ||v|| = 0 <=> v.v
= 0
/ a1 / a2 / a2-a1
M | b1 P | b2 u = MP = | b2-b1
\ c1 \ c2 \ c2-c1