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

enter image description here

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.

  • $\begingroup$ Is vector AB = A - B? God I am so stupid. Sorry this seems really obvious now $\endgroup$
    – samol
    Feb 5 '19 at 2:31
  • $\begingroup$ No, $\overrightarrow{AB}= B-A$. $\endgroup$
    – kccu
    Feb 5 '19 at 2:32
  • $\begingroup$ I have marked it as the correct answer. I don't know how to face my linear algebra teacher. Thank you very much for helping me $\endgroup$
    – samol
    Feb 5 '19 at 2:40
  • $\begingroup$ Actually does the direction of the vector even matter? like vector AB vs vector BA. The length of projection should be same regardless of which direction no? $\endgroup$
    – samol
    Feb 5 '19 at 2:41
  • 1
    $\begingroup$ @samol - don't be too hard on yourself. $\endgroup$ Feb 5 '19 at 3:21

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