Dot Product

Dot Product looks like this:
u * v = <x1, y1> * <x2, y2> = x1x2 + y1y2
If it equals 0, then the vectors are perpendicular.
If the vectors are multiples of each other then they're parallel.
Properties of Dot Products:
1. Commutative: u * v = v * u
2. Squared: u* u =! u^2; u * u = |u^2|
3. k(u * v) = ku * v
4. u * u = |u|^2
To find angle b/t two vectors: cos(theta) = u * v / |u| |v|
Examples:
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1.) Given u = (3, -6), v = (4, 2), w = (-12, -6), find u · v and v · w
and show that u and v are perpendicular and v and w are parallel.

(3)(4) + (-6)(2)
12 + (-12) = 0
-12/4 = -3


(4)(-12) + (2)(-6)
-48 + (-12) = -60
-6/2 = -3