I have this question when reading Linear Algebra http://www.math.nagoya-u.ac.jp/~richard/teaching/f2014/Lin_alg_Lang.pdf, page 39 - 40.
Consider a plane defined by the equation (X - P)· N == 0, and let Q be an arbitrary point. We wish to find a formula for the distance between Q and the plane as the figure here shows: question setup. The textbook gives reasoning as follows: textbook's reasoning
But I don't quite understand how to get (2) from (1). And all I have so far is the following:
The norm of the projection of Q-P onto N/||N||
= ||(Q-P)·(N/||N||)·(N/||N||) / ((N/||N||)·(N/||N||))||
= ||(Q-P)·(N/||N||)·(N/||N||)|| , since ((N/||N||)·(N/||N||)) = 1
Anyone might see what I am missing in my attempt to derive (2) from (1)? Thank you very much!