Angle between vectors

The term angle between vectors implies the smallest angle between vectors, one of which needs to be rotated to achieve collinearity with the other. In engineering, electrical engineering, and mathematical calculations, the angle between vectors is expressed through cos α equal to the ratio of the multiplied scalar values a and b to the product of the vector modules |a| and |b|.

Modules are found by extracting the root from the sum of the squares of the vector coordinate values. Example: determining the angle between vectors with coordinates a = {3; 4} and b = {4; 3}.
Scalar product 3 x 4 + 4 x 3 = 24,
|a| = root (3 squared + 4 squared) = 5,
|b| = root (4 squared + 3 squared) = 5,
cos α = 0,96.

The online calculator allows you to find angles between vectors not only in two-dimensional but also in three-dimensional space. The resulting information is provided in both degrees and radians.