Since u · v = |u||v| cos θ and all vectors in this problem have length 1.0, u · v = cos θ.
The dot product of au · bu is the cosine of the angle between au and bu, which can be read off the diagram as 0.866.
The dot product of au · cu is the cosine of the angle between au and cu, which can be read off the diagram as 0.500.
bu is closer in orientation to au so au · bu is the larger.
Remember: cos 30° = 0.866, sin 30° = 0.5, cos 60° = 0.5, and sin 60° = 0.866.
The dot products are:
So by using vectors of length one, the effect of length is removed and the dot product is larger when a small angle separates the vectors.
What do you suppose happens when the vectors are in opposite directions, such as (1, 0)T and (-1, 0)T ?