Question

Equation of the plane perpendicular to the line $\frac{x}{1}=\frac{y}{1}=\frac{z}{3}$ and passing through the point (2, 3, 4) is.

• A. $x+2y+3z=9$
• B. $x+y+3z=17$
• C. $2x+3y+z=17$
• D. $3x+2y+z=16$

Answer 1

The correct option is B $x+y+3z=17$

The given line is parallel to a vector whose direction ratios are $1,1,3$

So if the plane is perpendicular to the given line, direction rations of normal of the plane will be $1,1,3$

Hence equation of plane passing through $(2,3,4)$ is given by

$(x-2)1+(y-3)1+(z-4)3=0$

$\Rightarrow x+y+3z=12+3+2$

$\Rightarrow x+y+3z=17$