Warning: this is an htmlized version!
The original is across this link,
and the conversion rules are here.
% (find-angg "LATEX/2016-2-GA-VR.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2016-2-GA-VR.tex"))
% (defun d () (interactive) (find-xpdfpage "~/LATEX/2016-2-GA-VR.pdf"))
% (defun e () (interactive) (find-LATEX "2016-2-GA-VR.tex"))
% (defun u () (interactive) (find-latex-upload-links "2016-2-GA-VR"))
% (find-xpdfpage "~/LATEX/2016-2-GA-VR.pdf")
% (find-sh0 "cp -v  ~/LATEX/2016-2-GA-VR.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2016-2-GA-VR.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2016-2-GA-VR.pdf
%               file:///tmp/2016-2-GA-VR.pdf
%           file:///tmp/pen/2016-2-GA-VR.pdf
% http://angg.twu.net/LATEX/2016-2-GA-VR.pdf
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
%\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage{color}                % (find-LATEX "edrx15.sty" "colors")
\usepackage{colorweb}             % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
\usepackage{edrx15}               % (find-angg "LATEX/edrx15.sty")
\input edrxaccents.tex            % (find-angg "LATEX/edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-dn4ex "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-angg ".emacs.papers" "latexgeom")
% (find-latexgeomtext "total={6.5in,8.75in},")
\usepackage[%total={6.5in,4in},
            %textwidth=4in,  paperwidth=4.5in,
            %textheight=5in, paperheight=4.5in,
            a4paper,
            top=1.5in, left=1.5in%, includefoot
           ]{geometry}
%
\begin{document}

\catcode`\^^J=10
\directlua{dednat6dir = "dednat6/"}
\directlua{dofile(dednat6dir.."dednat6.lua")}
\directlua{texfile(tex.jobname)}
\directlua{verbose()}
%\directlua{output(preamble1)}
\def\expr#1{\directlua{output(tostring(#1))}}
\def\eval#1{\directlua{#1}}
\def\pu{\directlua{pu()}}

\directlua{dofile "edrxtikz.lua"} % (find-LATEX "edrxtikz.lua")
\directlua{dofile "edrxpict.lua"} % (find-LATEX "edrxpict.lua")
%L V.__tostring = function (v) return format("(%.3f,%.3f)", v[1], v[2]) end

\def\V(#1){\VEC{#1}}
\def\pla{{\mathsf{pla}}}




%   ____      _                    _ _           
%  / ___|__ _| |__   ___  ___ __ _| | |__   ___  
% | |   / _` | '_ \ / _ \/ __/ _` | | '_ \ / _ \ 
% | |__| (_| | |_) |  __/ (_| (_| | | | | | (_) |
%  \____\__,_|_.__/ \___|\___\__,_|_|_| |_|\___/ 
%                                                

{\setlength{\parindent}{0em}
\footnotesize
\par Geometria AnalÃtica
\par PURO-UFF - 2016.2
\par VR - 23/jan/2017 - Eduardo Ochs
\par Respostas sem justificativas nÃo serÃo aceitas.
\par Proibido usar quaisquer aparelhos eletrÃ∧nicos.
% \par VersÃo: 14/mar/2016
% \par Links importantes:
% \par \url{http://angg.twu.net/2015.2-C2.html} (pÃgina do curso)
% \par \url{http://angg.twu.net/2015.2-C2/2015.2-C2.pdf} (quadros)
% \par \url{http://angg.twu.net/LATEX/2015-2-C2-material.pdf}
% \par {\tt eduardoochs@gmail.com} (meu e-mail)
}

\bsk
\bsk

\setlength{\parindent}{0em}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\B       (#1 pts){{\bf(#1 pts)}}
% Usage:
% 1) \T(Total: 2.34 pts) Foo
% a) \B(0.45 pts) Bar

\unitlength=5pt
\def\closeddot{\circle*{0.6}}
\def\pictline#1{{\linethickness{1.0pt}\expr{Line.new(#1):pict()}}}



1) \T(Total: 2.0 pts) Verdadeiro ou falso? Justifique.

a) \B(1.0 pts) $\Pr_{\uu} (3\uu) = 3\uu$.

b) \B(1.0 pts) Se $\uuâ\vv$ entÃo
   $\Pr_{\uu} (4\uu+5\vv) +
    \Pr_{\vv} (4\uu+5\vv)
            = (4\uu+5\vv)$.

\bsk
\bsk

2) \T(Total: 2.0 pts) Sejam $r=\setofxyst{y=-2-2x}$, $A=(-1,5)$,
$B=(-1,4)$, $C=(-1,3)$, $D=(-1,2)$, $E=(-1,1)$, $F=(-1,0)$,
$G=(-1,-1)$, $H=(-1,-2)$, e sejam $A'$ o ponto de $r$ mais prÃximo de
$A$, $B'$ o ponto de $r$ mais prÃximo de $B$, e assim por diante.

a) \B(0.5 pts) Encontre $A'$.

b) \B(0.7 pts) Encontre $B'$.

c) \B(0.8 pts) Calcule $d(A,r)$, $d(B,r)$, $d(C,r)$, $d(D,r)$,
$d(E,r)$, $d(F,r)$, $d(G,r)$, $d(H,r)$.



\bsk
\bsk

3) \T(Total: 2.0 pts) Represente graficamente as cÃ∧nicas com as
equaÃÃes abaixo. Algumas sÃo degeneradas.

\begin{tabular}[t]{lcl}
a) \B(0.2 pts) $(x-3)^2=1$ \\
b) \B(0.2 pts) $(x+y)^2=1$ \\
c) \B(0.3 pts) $(x-3)^2 + (x+y)^2 = 0$ \\
d) \B(1.0 pts) $(x-3)^2 + (x+y)^2 = 1$ \\
\end{tabular}
\quad
\begin{tabular}[t]{lcl}
e) \B(0.3 pts) $(x-3)(x+y)=0$ \\
f) \B(1.0 pts) $(x-3)(x+y) = 1$ \\
\end{tabular}




\bsk
\bsk

4) \T(Total: 2.0 pts) Uma aplicaÃÃo do `$Ã$' que nÃo foi mencionada na
p.35 Ã a seguinte. Se $A,B,Câ\R^3$, definimos:
%
$$\begin{array}{c}
  \pla(A,B,C) \;:=\; \setofxyzst{w_1x+w_2y+w_3z = w_1A_1 + w_2A_2 + w_3A_3} \\[5pt]
  \text{(onde $\ww := \Vec{AB}Ã\Vec{AC}$)} \\
  \end{array}
$$
%
\noindent
A aplicaÃÃo Ã: {\sl se $A,B,C$ nÃo sÃo colineares entÃo $\pla(A,B,C)$
  Ã o plano contendo $A$, $B$, e $C$.}

\ssk

a) \B(0.2 pts) Sejam $A=(2,0,0)$, $B=(0,3,0)$, $C=(0,0,4)$,
$Ï=\pla(A,B,C)$. Expresse $Ï$ na forma $\setofxyzst{ax+by+cz=d}$. Quem
sÃo $a$, $b$, $c$, $d$?

b) \B(0.8 pts) Encontre o valor de $z$ que faz com que o ponto
$(1,1,z)$ pertenÃa ao $Ï$ do item anterior.

c) \B(0.2 pts) Teste se $(2,3,4) â \pla((1,0,0),\,(2,0,0),\,(3,0,0))$.

d) \B(0.8 pts) Explique o que acontece quando $A,B,C$ sÃo colineares.
O que à $\pla(A,B,C)$ neste caso?


\bsk
\bsk

5) \T(Total: 2.0 pts) Calcule a distÃncia entre
$r=\setofst{(x,4-2x,0)}{xâ\R}$ e $r'=\setofst{(3-z,3-z,z)}{zâ\R}$.





% \newpage
% 
% $\vcenter{\hbox{\beginpicture(-2,-2)(2,2)%
%     \pictaxes%
%     \pictline{v(-1,0), v(1,-2), -2, 2}
%    \end{picture}%
%  }}$



% 1) \T(Total: 2.34 pts) Foo
% a) \B(0.45 pts) Bar


\end{document}

% Local Variables:
% coding: utf-8-unix
% ee-anchor-format: "«%s»"
% End: