Dot Product

DOT Product: u*v= * = x1x2+y1y2 -- If the dot product equals zero, then the vectors are orthogonal, which means perpendicular. -- If the vectors are multiples of each other, then they are parallel. -- To find the angle between two vectors, use the formula: cos(theta)= u*v/magnitudeU * magnitudeV -- Properties of the DOT product: 1.  commutative: u * v = v * u 2.  squared u * u does not equal u^2 u * u = magnitude of u^2 3.  K(u * v)= Ku * v doesn't distribute 4.  u * (v+w) = u * v + u * w _____________________________________________________________________ Ex.1: u(3, -6) v(4,2) w(-12,-6) -Find the u*v and v*w. Show that u and v are orthogonal and v and w are parallel u*v = 3(4) + -6(2) = 0 which means they are perpendicular because it equals 0 v*w = -12(2) + 2(-6) = -60 w/v = -12/4 = -3 -6/2 = -3 : They are multiples of each other therefore they are parallel