Question

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

• A. $2x+3y+z=17$
• B. $x+2y+3z=9$
• C. $3x+2y+z=16$
• D. $x+2y+3z=20$

Answer 1

The correct option is D

$x+2y+3z=20$

Explanation for the correct option:

Given,

The direction ratios of the lines are $=\left(\hat{i},2\hat{j},3\hat{k}\right)$

According to the question,

given line is perpendicular to the plane

$\Rightarrow$The direction ratios of the plane are also $=\left(\hat{i},2\hat{j},3\hat{k}\right)$

$\therefore$The equation of plane passing through $(2,3,4)$ is

$a(x-2)+b(y-3)+c(z-4)=0$

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

$\Rightarrow$ $\mathit{x}\mathbf{+}\mathbf{2}\mathit{y}\mathbf{+}\mathbf{3}\mathit{z}\mathbf{}\mathbf{=}\mathbf{}\mathbf{20}$

Hence, Option ‘D’ is Correct.