Question

A plane passing through the line joining the points $A(1,-3,5)$ and $B(4,1,-1)$ is turned about $AB$ till it passes through the origin. The equation of the plane in the new position is

• A. $3x+4y-6z=0$
• B. $2x-21y+13z=0$
• C. $2x-21y-13z=0$
• D. none of these

Answer 1

The correct option is C $2x-21y-13z=0$

Equation of plane passing through origin is given by,
$ax+by+cz=0$
Also plane passing through $A(1,-3,5)$
$\Rightarrow a-3b+5c=\mathrm{0......}\left(1\right)$
It also passes through $B(4,1,-1)$
$\Rightarrow 4a+b-c=\mathrm{0.....}\left(2\right)$
Solving $\left(1\right)$ and $\left(2\right),$ we get

$a=\frac{-2c}{13},b=\frac{21c}{13}$
Hence, required plane is
$2x-21y-13z=0$