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  • Please solve RD Sharma class 12 chapter 28 The Plane exercise Fill in the blank question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 28 The Plane exercise Fill in the blank question 9 maths textbook solution

Answers (1)

Answer:

 (2,2,2)

Hint:

 Let its intercept be λ

Given:

Sum of the reciprocals of its intercepts on the coordinates axis is 1/2 

Solution:

Let the equation of the variable plane be

\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=\lambda \dots \dots \dots \dots(1)

The intercepts on the coordinate axes are a,b,c

Let the sum of reciprocals of intercept in constant =λ

Therefore,

\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\lambda \Rightarrow \frac{(\frac{1}{\lambda })}{a}+\frac{(\frac{1}{\lambda })}{b}+\frac{(\frac{1}{\lambda })}{c}=\lambda

\left ( \frac{1 }{\lambda },\frac{1 }{\lambda },\frac{1 }{\lambda } \right )

lies on the plane (1)

Hence, the variable plane (1) always passes through

the fixed point

\left ( \frac{1 }{(\frac{1}{2})},\frac{1 }{(\frac{1}{2})},\frac{1 }{(\frac{1}{2})}\Rightarrow 2,2,2 \right )

Posted by

Gurleen Kaur

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