Angle between lines
This calculator is designed for calculating the angle between two lines online.
Two lines can have three variants of relative positioning to each other. They can coincide, be parallel, or intersect. For determining the angle between lines, the most interesting case is the angle between intersecting (or intersecting) lines.
If two lines have a common point, such lines are called intersecting. The intersection point divides each of the lines into two rays. Between the rays of intersecting lines, four angles are formed (two acute and two obtuse). Thus, the angle between two intersecting lines – is the smallest angle (acute), formed at the intersection of these lines. It should be noted that if the value of one of the angles is known, the values of the other three angles can be easily found thanks to the properties of vertical and adjacent angles.
To find the angle between two lines using this calculator, you need to enter the coefficients in the equations of the lines and press the button «Calculate».
If the lines are given by the following equations:
then the direction vectors of these lines will be equal:
We use the formula for the scalar product of two vectors:
from this formula we will get:
Express the angle φ :
From the last formula we will get:
