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 = -6i -8j v middot w = (Simplify your answer.) The angle between v and w is theta =^degree. (Simplify your answer.) The vectors v and w are

Solution

a) v.w = (3i + 4j).(-6i - 8j) = -18 - 32 = -50

b) |v||w|cos(theta) = v.w

cos(theta) = -50/(5 x 10) = -1

theta = 180^o

c) parallel (actually antiparallel)