Angle Between Two Vectors Formula
Formula
Summary
The angle between two vectors can be calculated by the arc cosine function of the dot product of the two vectors divided by the product of their respective magnitudes.
Expression  Description 

The angle between the two vectors  
The first vector  
The second vector 
Usage Notes
Dot Product
The dot prodcut of two vectors is calculated by summing together the product of corresponding elements.
Magnitude of Vector
The magnitude of a vector is given by the square root of the sum of its components squared.
To find the angle between two vectors one can use the formula below:
Steps

Substitute the vectors into the formula.

Compute dot product and magnitudes.

Evaluate multiplication, exponent and squareroot expressions. Since the numerator goes to zero, the whole expression goes to zero.

Compute the arccosine.

The angle is radians or .