For the following vectors a find the dot product v middot w

For the following vectors, (a) find the dot product v middot w; (b) find the angle between v and w; (c) state whether the vectors are parallel, orthogonal, or neither. v = 3i - 4j, w = -18i + 24j (a) v middot w = (Simplify your answer.)

Solution

v=3i-4j

w=-18i+24j

v.w=3*(-18) +(-4)*24=-54-96=-150

|v|=sqrt(9+16)=5

|w|=sqrt(324+576) =30

cos theta=v.w/(|v||w|)=-150/150=-1=180°

So they are neither parallel nor orthogonal