# What is the value range from a dot-product between two normalized vectors?

I've recently learned about the existence of dot product and I was wanted to know how to determine the value range between two normalized vectors.

• Not sure I understand the question. Is this what you're looking for: chortle.ccsu.edu/vectorlessons/vch09/vch09_6.html ? Jan 31 '19 at 2:44
• Normalized vectors are between -1:1, and the dot product is ax*bx+ay*by It's fairly straight forward. Jan 31 '19 at 4:02

Because the dot product is, geometrically, the product of the magnitudes of the vectors and the cosine of the angle between them ($$\\vert{a}\vert\vert{b}\vert \cos{\theta} \$$) it also useful for finding $$\\theta\$$: it's just $$\\arccos{(a \cdot b)}\$$ since the magnitudes of the vectors are both one.