# How to calculate the length orthogonal projection of a point onto a line

Let's say you have point A, B, C, these are represented by vectors:

($$x_a$$, $$y_a$$), ($$x_c$$, $$y_c$$), ($$x_c$$, $$y_c$$)

Imagine you draw a line across B and C, how do I find the length of the orthogonal projection of A to the line represented by B,C

I know how to calculate the orthogonal projection of 2 vectors (Which I learned in undergrad linear algebra). But I don't think I learned how to project a vector onto a line that is formed by 2 vectors

The line whose length you have labeled as "$$?$$" is the vector $$\overrightarrow{AB}-\text{proj}_{\overrightarrow{BC}}(\overrightarrow{AB})$$. So if you can calculate the projection of one vector onto another, then you can calculate the length of that line.
• No, $\overrightarrow{AB}= B-A$.