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  • Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.2 question 3

Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.2 question 3

Answers (1)

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Answer:

Equation of plane is \frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=3

Hint:

First using centroid, identify the values of  a, b  & c  then using  \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1  , find equation of plane.

Given:

Plane meets axis in A, B\; \& \; C.

Explanation:

Assume, A=(a, 0,0), B=(0, b, 0), \& \; C=(0,0, c)

Here, centroid of triangle AB  is  \left ( \alpha ,\beta, \gamma \right )

Now,

centroid =\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}, \frac{z_{1}+z_{2}+z_{3}}{3}\right)

            \begin{aligned} &\Rightarrow(\alpha, \beta, \gamma)=\left(\frac{a+0+0}{3}, \frac{0+b+0}{3}, \frac{0+0+c}{3}\right) \\\\ &\Rightarrow \alpha=\frac{a}{3}, \quad \beta=\frac{b}{3}, \quad \gamma=\frac{c}{3} \\\\ &\Rightarrow a=3 \alpha, \quad b=3 \beta, \quad c=3 \gamma \end{aligned}

Put the values of A, B\; \& \; C.  in \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1

            \Rightarrow \frac{x}{3 \alpha}+\frac{y}{3 \beta}+\frac{z}{3 \gamma}=3

Here, equation of plane is

            \frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=3

 

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