Question

The equation of the plane passing through the points $P(1,1,1),Q(3,-1,2),R(-3,5,-4)$ is

• A. $x+y=2$
• B. $y+z=2$
• C. $z+x=2$
• D. $x+y+z=2$

Answer 1

The correct option is A $x+y=2$

Equation of plane is:
$\left|\begin{array}{ccc}x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\end{array}\right|=0$

Here, given points are
$P(1,1,1),Q(3,-1,2),R(-3,5,-4)$
So equation of plane is

$\left|\begin{array}{ccc}x-1& y-1& z-1\\ 3-1& -1-1& 2-1\\ -3-1& 5-1& -4-1\end{array}\right|=0\Rightarrow \left|\begin{array}{ccc}x-1& y-1& z-1\\ 2& -2& 1\\ -4& 4& -5\end{array}\right|=0\Rightarrow (x-1)(10-4)-(y-1)(-10+4)+(z-1)(8-8)=0\Rightarrow (x-1)6-(y-1)(-6)=0\Rightarrow x+y=2$