Vector Formulæ

New Vocabulary: Orthogonal = Perpendicular

     Vector Operations with Coordinates

Vector Addition: v + u = (a, b) + (c, d) = (a + c, b + d)

Vector Subtraction: v - u = (a, b)-(c, d) = (a - c, b - d)

Scalar Multiplication: kv = k(a, b) = (ka, kb)

     The Dot Product

 If v1 = (x1, y1) and v2 = (x2, y2) then the dot product, denoted by v1•v2 is defined by

v1•v2 = x1x2 + y1y2.

     Properties of the Dot Product

 1. u • v = v • u

 2. u • u = |u|²

 3. k(u • v) = (ku) • v

 4. u • (v + w) =  u • v + u • w