Question

Analytical geometry help needed here:
In the triangle ABC, height AH is constructed. Find coordinates of vector AH in the basis of vectors AB and AC.

Answer 1

Here's the picture:

Answer 2

so, AC is perpendicular to AB, right?

Answer 3

No, unfortunately it's an arbitrary triangle.

Answer 4

\[
\vec{AH'}=\vec{AH}-\frac{<\vec{AB},\vec{AH}>}{<\vec{AB},\vec{AB}>}\vec{AB}
\]
this is the orthonormal basis of AH on AB

Answer 5

Here is one way.

Answer 6

Thank you so much! :) @phi