Scalar Product in a Plane

u·u = x^2 + y^2 +2xy

||u||·||v||·sinθ

xx' + yy'

||u||·||v||·cosθ

||u|| = √(u^2) = √(x^2 + y^2)

||u|| = x + y

||u|| = x - y

||u|| = x^2 + y^2

u and v have the same sense

u and v have opposite sense

u is greater than v

u is less than v

u·v = v·u

u·(v+w)=u.v+u.w

u·v =u x v

u·v = 0 then u and v are parallel

u·(v + w) = u·v + v·w

u·(v + w) = u·v + u·w

(u+v)·(w-z)=

u·w-u·v+v·w-v·z

u·(v + w) = w·(v + u)

u^2 - 2·u·v + v^2

u^2 + v^2

u·v

0

their ratio is a constant

their dot product is zero

xx'+yy'+cos(theta)=0

a new vector

the sum of their components

their alignment

a real number

-0.8

0.8

0.64

36.87

u and v are parallel

u=kv

u and v are perpendicular

theta = -pi