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  • Provide solution for RD Sharma maths class 12 chapter The Plane exercise 28.15 question 2

Provide solution for RD Sharma maths class 12 chapter The Plane exercise 28.15 question 2

Answers (1)

Answer:   \left(\frac{73}{25},-\frac{6}{5}, \frac{39}{25}\right)

Hint:

Suppose point P(1,2,-1), Let P M \perp \text { Plane. }

Direction = (3,-5,4)

P(1,2,-1)

                                        

 

Given:

 

Find the reflection of the point (1,2,-1) in the plane 3x-5y+4z=5

 

Solution:

Direction of line =(3,-5,4)=(3,-5,4)=(3,-5,4)= (3,-5,4)
Equation of line   \frac{x-1}{3}=\frac{y-2}{5}=\frac{3+1}{4}=x


x=3\lambda +1,y=-5x+2,z=4\lambda -1


Put in (3x-5y+4z=5)


3(3\lambda +1)-5(-5\lambda +2)+4(4\lambda -1)=5

\begin{aligned} &9 \lambda+3+25 \lambda-10+16 \lambda-4=5 \\\\ &50 \lambda=16 \\\\ &\lambda=\frac{16}{50}=\frac{8}{25} \end{aligned}

So that
\begin{aligned} &x=3\left(\frac{8}{25}\right)+1=\frac{73}{25} \\\\ &y=-5\left(\frac{8}{25}\right)+2=\frac{6}{5} \\\\ &z=4\left(\frac{8}{25}\right)-1=\frac{39}{25} \end{aligned}

coordinate \left(\frac{73}{25}, \frac{-6}{5}, \frac{39}{25}\right) Ans.

Posted by

infoexpert26

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