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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 11

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 11

Answers (1)

Answer:

 Option (c)

Hint:

 Use the centroid formula.

Given:

 \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k

Solution:

A plane meets the co-ordinate area of (A, B, C) such that the centroid of \Delta ABC  is the point (a,b,c).

Let the co-ordinate of the point

 A(\alpha , 0, 0),\: B(0,\beta ,0),\: C(0,0,\gamma )

By the centroid formula,

\begin{aligned} &a =\frac{\alpha +0+0}{3}\\ &\Rightarrow \alpha =3a\\ &b=\frac{0+\beta +0}{3}\\ &\Rightarrow \beta =3b\\ &c=\frac{0+0+\gamma }{3}\\ &\Rightarrow \gamma =3c \end{aligned}

The Intercept form of the plane–

\frac{x}{p}+\frac{y}{q}+\frac{z}{r}=1

If the plane makes intercepts at (p, 0, 0), (0, q, 0) and (0, 0, r) with the axes x, y, z respectively.

Here,

p=\alpha =3a,\: q=\beta =3b,\: r=\gamma =3c

So, the equation of the plane is,

\begin{aligned} &\frac{x}{3a}+\frac{y}{3b}+\frac{z}{3c}=1\\ &\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3 \qquad \qquad \qquad \dots(1) \end{aligned}

By comparing the equation (1) with given equation of the plane

\begin{aligned} &\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k \end{aligned},

we get k = 3.

Posted by

Gurleen Kaur

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