How to find out the angle between two straight lines if the coordinates through which they pass are known?

Question

Geometry

There is an XY coordinate plane. There are two lines and the coordinates of the points through which these lines pass are known. How to find out the degree measure of the angle that these lines form?

Here is a picture of what it might look like

Answer 1

Get 2 vectors along these lines (if the lines are given parametrically - you already know them, if Ax+By+C=0, then this is {-B,A}). Now the angle between the two vectors a and b is your desired angle. Here we must remember that the vector product is |a|*|b|*sin x, and the scalar product is |a|*|b|*cos x. Now you know the sin and cos of the desired angle (by dividing the scalar / vector product by the lengths of the vectors). You can feed these values ​​to atan or some other inverse trigonometric function. But in practice, the angle itself is rarely needed, it is needed in the calculations of its sin and cos, and you already know them.