I'm reading a differential geometry book named "Elementary geometry of differentiable curves: An undergraduate introduction" written by Gibson.

I'm on page 2. On that page, 4 properties of scalar product(dot product) of vectors are given.

One of them is:

I know the proof of this and the proof shows that the statement is true for

I accept this.

But if

isn't it definite that

has to be equal to

and not greater than

?

Can anyone find a

such that when

then

is greater than

?

Why did the author said that

? Why did he mention greater and equal, and not just equal to

?