This calculator finds the angle between two vectors given their coordinates. The formula and the explanation can be found below the calculator
Finding the angle between two vectors
We will use the geometric definition of the Dot product to produce the formula for finding the angle.
Geometrically the dot product is defined as
thus, we can find the angle as
To find the dot product from vector coordinates we can use its algebraic definition.
Thus, for two vectors, and , formula can be written as
This is the formula used by the calculator