Dot Product

Dot Product: u*v = <x1,y1> * <x2,y2> = x1 x2 + y1 y2
-If the dot produect equals 0 thent he vecotrs are orthogonal (perpendicular)
-If the vectors are multiples fo each other they are parallel
-To find the angle b/w two vectors cos theta = u*v over the magnitude of u and v


Example 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

Example 2: To the nearest degree find the angle between the vectors (1,2) and (-3,1)

u*v = 1(-3) + 2(1) = -1

magnitude of u = square root of 5
magnitude of v = the square root of 10

-Now following the formula in point 3 we need to do cos theta
1/ square root of 5 times square root of 10
theata = inverse of cos(-1/ square root of 50) = 81.867
-You find it in the 1st and 3rd quadrents: 98.130 and 261.87

--Daniellee