Getting angle between two vector3's?

We can use the fact that the dot product of two vectors has two equivalent definitions.

The first definition is the sum of the products of the components, and ROBLOX provides this for you: If a and b are vectors, then the dot product of a and b is a:Dot(b).

The second definition is the product of the vectors' magnitudes and the cosine of the angle between them. So we have some simple algebra here:

-- Let a and b be vectors and d be the dot-product of them.
-- t is the angle for which we are solving, and |u| is taken to mean the
-- magnitude of u (in ROBLOX, u.magnitude)

-- |a| * |b| * cos(?) = d
-- cos(t) = d / (|a| * |b|)
-- t = arccos(d / (|a| * |b|))

-- To clean this math up further, we can make a and b be
-- unit vectors, so that their magnitudes are one and don't matter.
-- cos(t) = d
-- t = arccos(d)

-- So here it is in Lua.


-- a and b are the unit vectors
local theta = math.acos( a.unit:Dot(b.unit) );
-- theta is now the angle between a and b, measured in radians.