Question

sabendo que os pontos a(4,0,0) b(0,0,2) c(0,3,0) e d(4,3-2) são coplanares, calcular a área do quadrilátero abcd

Answer 1

A(4,0,0)
B(0,0,2)
C(0,3,0)
D(4,3,-2)

AB e AD: 

AB = (4,0,-2)
AD = (0,3,2 )

$\left[\begin{array}{ccc}i&j&k\\4&0&-2\\0&-3&2\end{array}\right] \\ i=6\\ j=-8 \\-12$
$\\\\\\V=(6,-8,-12)\\ |V|= \sqrt{6^2+8^2+12^2} \\ |V|= \sqrt{244}$

MMC:
244|2
122|2
061

$\sqrt{144} = \sqrt{2^2.61}= 2 \sqrt{61}$

Resposta: $2 \sqrt{61}$