Determine whether the vectors u and v are parallel, orthogonal, or neither. u = < 1, -2> , v = < -4, 8> a) orthogonal b) neither c) parallel

U dot v = <1,-2> dot <-4,8>
u dot v = 1*(-4) + (-2)*8
u dot v = -4 - 16
u dot v = -20
The nonzero dot product tells us that u and v are not orthogonal

u = k*v
<1,-2> = k*<-4,8>
<1,-2> = <-4k, 8k>
1 = -4k implies that k = -0.25
-2 = 8k implies that k = -0.25
The fact we get the same k value each time tells us the two vectors are parallel (they point in the same direction on the compass). One vector is a scaled version of the other. 

C) Parallel