i have the following problem:
Given are points P1 and P2. I also have the direction, in the image noted as D, given as a unit vector. Additionally, I have the angles alpha and gamma and I know that beta is 90°.
Now I Want to find point P3 which lies on the direction vector D. The direction vector and the line from P3 to P2 form a 90° angle.
Do you have ideas how to solve this? Probably the problem is quite simple. Unfortunately I'm not very good at math, so excuse my question.
Thank you in advance
In the vector form the answer reads: $${\mathbf P}_3= {\mathbf P}_1+(({\mathbf P}_2-{\mathbf P}_1)\cdot{\mathbf D}){\mathbf D}. $$
As clarified in comments the angle $\alpha $ is not a free parameter and is "hiďden" in the dot product.