6.4

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Geometric Concepts

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What is a dot product?

The product of a vector and a scalar that yields a scalar

Dot Product of u = and v=

u*v=u1v1 + u2v2

Vector Components

w1=projvU

u=w1+w2

u and v are orthogonal if u * v = 0

w2=u-w1

w1 and w2 are orthogonal and w1 is parallel to v

u and v are non zero vectors

Angle Between Two Vectors

cos θ=(u*v)/(ll u ll ll v ll)

Properties of the Dot Product

u*(v+w)=u*v+u*w

0*v=0

u*v=v*u

c(u*v)=cu*v=u*cv

v*v=llvll^2

Definition of Work

Work= F * PQ--->

Projection of u onto v

ProjvU=((u*v)/( ll v ll^2)v

The Dot Product of Two Vectors