Why can dot products be negative if magnitudes are always positive?

[Pupil]

Homework Statement

Vector A and four other vectors that have the same magnitude but differ in orientation. a) Which of those other four vectors have the same dot product with A? b) Which have a negative dot product with A?
http://img195.imageshack.us/img195/7079/40191924.th.jpg
(Those circle things between the arrows are supposed to be thetas. I suck at drawing quickies in paint.)

Homework Equations

a*b = abcos(theta)

The Attempt at a Solution

For a) I recognized that they would all have the same dot product with a, since the magnitude of all the vectors are the same, as is their angle. What I don't get is the answer to b. It says D and E. Shouldn't the dot products all be positive? In the equation a and b are positive (and always will be), and cos(theta) is positive in this case, how would the dot product turn out to be negative?

 

[slider142]

What is the angle between D and A?

 

[Pupil]

What is the angle between D and A?

180 - theta.

 

[slider142]

By the image, it looks like $\theta$ is acute, so 180 - $\theta$ must be obtuse. From this, you should be able to guess the sign of the cosine of the angle.

 

[Pupil]

Yeah, I understand where I went wrong. Thanks.