Little problem with \tkzMarkRightAngle

Question

I have this code:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{tikz} 
\usetikzlibrary{matrix,decorations.pathreplacing}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}%[dot/.style={fill,circle,inner sep=1.5pt}]
\path
  (30:5) node [label=below right:$v_i\in M_2$,yshift={5pt}]{} coordinate (A)
  (30:7) coordinate (a)
  (-20:5) node [label=above right:$u_i\in M_1$,yshift={-10pt}]{} coordinate (B)
  (-20:7) coordinate (b)
  (0:0) node {} coordinate(P);

\path
  (0:0) node {}
coordinate(W)
  (90:4) node [label=left:$w_i$]{}
coordinate (Z)
  (90:6) coordinate (z);

\node (Q) at ($(P)!(A)!(B)$) {};
\node (R) at ($(P)!(B)!(A)$) {};

\draw[<->]  (P) -- (A);
\draw (P) -- (a);
\draw  (P) -- (b);
\draw[->] (P) -- (B);
\draw[->] (P) -- (Z);
\draw (P) -- (z);

\draw[purple!70!black,dashed] (A) -- (Q);
\draw[green!70!black] (B) -- (R);
\tkzMarkRightAngle(A,Q,P)
\tkzMarkRightAngle(B,R,P)

\tkzMarkAngle[size=0.75cm,color=cyan,label=$\theta$](B,P,A);
\end{tikzpicture} }
\end{document}

to get:

As you can see, the squares for right angles isn't appears good. There are something that I make bad? Any option or libraries is not necessary?

PD: I read A right-angle mark not displayed properly but the problem continues making %[dot/.style={fill,circle,inner sep=1.5pt}].

PD: I have another packages but it has nothing to do with this graphic.

PD: If some package is missing, sorry.

Answer 1

Don't use \nodes for Q and R; use \coordinates instead; a \node has an inner sep and outer sep which cause the problem.

The code:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage{tikz} 
\usetikzlibrary{matrix,decorations.pathreplacing}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}

\begin{document}
\begin{tikzpicture}%[dot/.style={fill,circle,inner sep=1.5pt}]
\path
  (30:5) node [label=below right:$v_i\in M_2$,yshift={5pt}]{} coordinate (A)
  (30:7) coordinate (a)
  (-20:5) node [label=above right:$u_i\in M_1$,yshift={-10pt}]{} coordinate (B)
  (-20:7) coordinate (b)
  (0:0) node {} coordinate(P);

\path
  (0:0) node {}
coordinate(W)
  (90:4) node [label=left:$w_i$]{}
coordinate (Z)
  (90:6) coordinate (z);

\coordinate (Q) at ($(P)!(A)!(B)$);
\coordinate (R) at ($(P)!(B)!(A)$);

\draw[<->]  (P) -- (A);
\draw (P) -- (a);
\draw  (P) -- (b);
\draw[->] (P) -- (B);
\draw[->] (P) -- (Z);
\draw (P) -- (z);

\draw[purple!70!black,dashed] (A) -- (Q);
\draw[green!70!black] (B) -- (R);
\tkzMarkRightAngle(P,Q,A)
\tkzMarkRightAngle(P,R,B)

\tkzMarkAngle[size=0.75cm,color=cyan,label=$\theta$](B,P,A);
\end{tikzpicture}
\end{document}

As a side note, since you are loading tkz-euclide and using some of its features, you could use the package commands and features for most of the things you are doing directly with TikZ; for example, instead of

\coordinate (Q) at ($(P)!(A)!(B)$);
\coordinate (R) at ($(P)!(B)!(A)$);

you can use

\tkzDefPointBy[projection=onto P--B](A)
\tkzGetPoint{Q}
\tkzDefPointBy[projection=onto P--A](B)
\tkzGetPoint{R}