VECTORS

This past week in advanced math we learned about Dot product.
This lesson was pretty simple. 


Dot product= u*v = <x1,y1> * <x2,y2> = x1 x2 + y1 y2


Here are the rules to know when approaching dot product equations:


-If the dot product equals 0, then the vectors are orthogonal (perpendicular).


-If the vectors are multiples of each other, then they are parallel.


-In order to find the angle b/w two vectors use: cos theta = u*v over the magnitude of u and v




Example 1: u(2, -1) v(3,6) w(-5,3)


Find the u*v and v*w. Show that u and v are orthogonal and v and w are parallel


u*v = 2(3) + -1(6) = 0 which means they are perpendicular because it equals 0


v*w = 3(-5) + 6(3) = 3


w/v = 18/-15 = -6/5
-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 and 261


wink ;-)