vectors

Find u*v and v*w.  Show that u and v are orthogonal and v and w are parallel.
u=(3,-6) v=(4,2) w=(-12,-6)
u*v=3(4)+-6(2)=0
v*w=4(-12)+2(-6)=-60
w/v=-12/4=-3
        -6/2=-3
We are given 3 different points:u,v, and w.  First it tells you to find u*v and v*w.  These are called dot products.  To solve a dot product, you have to multiply your x1 and x2 together and your y1 and y2 together.  You get those two products and add them together to get your answer.  If the dot product equals 0, then the vectors are orthogonal.  Orthogonal means perpendicular.  The dot product of u and v equals zero, so that product is orthogonal.  Now it says to show that v and w are parallel.  If the vectors are multiples of each other they are parallel.  When you divide -12 by 4, you get -3, and when you divide -6 by 2, you get -3 also.  -3 are multiples of each other, so v and w are parallel.