Question

The equation of the plane passing through the points $(1,2,3),(-1,4,2)$ and $(3,1,1)$ is

• A. 5x + y +12z -23 = 0
• B. 5x + 6y + 2z = 23
• C. 5x + 6y - 2z = 23
• D. x + y + z =13
• E. 2x + 6y +5z = 7

Answer 1

Answer: (B)

Given that,
$x_1=1,y_1=2,z_1=3$
$x_2=-1,y_2=4,z_2=2$
and $x_3=3,y_3=1,z_3=1$
Equation of plane passing through these points is
$\left|\begin{array}{ccc}x-1& y-2& z-3\\ -2& 2& -1\\ 2& -1& -2\end{array}\right|=0$
$\Rightarrow (x-1)(-4-1)-(y-2)(y+2)+(z-3)(2-4)=0$
$\Rightarrow (x-1)(-5)-(y-2)(6)+(z-3)(-2)=0$
$\Rightarrow -5x+5-6y+12-2z+6=0$
$\Rightarrow -5x-6y-2z+23=0$
$\Rightarrow 5x+6y+2z-23=0$
$\Rightarrow 5x+6y+2z=23$