I am struggling with a problem and would appreciate any help or guidance. The problem involves finding the length of the orthogonal projection of a line segment onto a line.
The problem gives us a line $l$ and two points $A$ and $B$ in a plane. The length of the line segment $AB$ is 20 units. The distance from point $A$ to line $l$ is 2 units, and the distance from point $B$ to line $l$ is 14 units. We need to determine the length of the orthogonal projection of the line segment $AB$ onto the line $l$.
I have attempted to solve the problem using the formula for the projection of a vector onto a line, but I am unsure how to proceed from there. I would greatly appreciate any suggestions or insights on how to approach this problem.
Thank you in advance for your help!