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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!

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