Question

The equation of the plane passing through the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3}$ and parallel to the direction whose direction numbers are $3,4,2$ is

• A. $14x-5y-11z=19$
• B. $3x+4y+2z+1=0$
• C. $2x-y+3z=3$
• D. none of these

Answer 1

The correct option is A $14x-5y-11z=19$

Equation of plane passing through given line is given by,
$a(x-1)+b(y+1)+cz=0$
Also direction ratio of line are $2,-1,3$
$\Rightarrow 2a-b+3c=\mathrm{0......}\left(1\right)$
and plane is parallel to direction with dr $3,4,2$
$\Rightarrow 3a+4b+2c=\mathrm{0.....}\left(2\right)$
Solving (1) and (2), we get $a=\frac{-14c}{11},b=\frac{5c}{11}$
Hence, required plane is
$14x-5y-11z=19$