13.3 Dot Product

<a₁,a₂> ^. <b₁, b₂> = a₁b₁ + a₂b₂

Application 1: cos T = ( a ^. b ) / ( ||a|| ||b|| )

a and b are orthogonal iff a ^. b = 0

Application #2 Angles and direction cosines

Application #3 Projections

Application #4: Work W = |F| |D| cos T = F^.D where D is the displacement vector

Sam exerts a horizontal force of 25 lbs on a box as he pushes it up a ramp that is 10 ft long and inclined at an angle of 20 degrees above the horizontal.  Find the work done on the box. 

W= (25) (10) cos 20 = 235 ft-lb.