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  • A plane P meets the coordinate axes at A, B and C respectively. The centroid of is given to be (1,1,2). Then the equation of the line through this centroid and p

A plane P meets the coordinate axes at A, B and C respectively. The centroid of \Delta ABC is given to be (1,1,2). Then the equation of the line through this centroid and perpendicular to the plane P is :
Option: 1 \frac{x-1}{2}=\frac{y-1}{1}=\frac{z-2}{1}
Option: 2 \frac{x-1}{1}=\frac{y-1}{1}=\frac{z-2}{2}
Option: 3 \frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{1}  
Option: 4 \frac{x-1}{1}=\frac{y-1}{2}=\frac{z-2}{2}

Answers (1)

best_answer

\\\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \\ \\A \equiv(a, 0,0), B \equiv(0, b, 0), C \equiv(0,0, c) \\ \\\text {Centroid } \equiv\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(1,1,2)

a=3, b=3, c=6

\\\text { Plane: } \quad \frac{x}{3}+\frac{y}{3}+\frac{z}{6}=1 \\ \\ {\;\;\qquad\qquad2 x+2 y+z=6}

\begin{aligned} &\text {Line } \perp \text { to the plane }(\mathrm{DR} \text { of line }=2 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})\\ &\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{1} \end{aligned}

 

Posted by

himanshu.meshram

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