The Dot Product of Two Vectors
Projection of u onto v
ProjvU=((u*v)/( ll v ll^2)v
Definition of Work
Work= F * PQ--->
Properties of the Dot Product
v*v=llvll^2
c(u*v)=cu*v=u*cv
u*v=v*u
0*v=0
u*(v+w)=u*v+u*w
Angle Between Two Vectors
cos θ=(u*v)/(ll u ll ll v ll)
Vector Components
u and v are non zero vectors
w1 and w2 are orthogonal and w1 is parallel to v
w2=u-w1
u and v are orthogonal if u * v = 0
u=w1+w2
w1=projvU
What is a dot product?
The product of a vector and a scalar that yields a scalar
Dot Product of u = <u1,u2> and v=<v1,v2>
u*v=u1v1 + u2v2