Angle Between Two Vectors Formula
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.
|The angle between the two vectors|
|The first vector|
|The second vector|
The dot prodcut of two vectors is calculated by summing together the product of corresponding elements.
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:
Substitute the vectors into the formula.
Compute dot product and magnitudes.
Evaluate multiplication, exponent and square-root expressions. Since the numerator goes to zero, the whole expression goes to zero.
Compute the arc-cosine.
The angle is radians or .