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  • Please solve RD Sharma class 12 chapter 28 The Plane exercise multiple choice question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 28 The Plane exercise multiple choice question 17 maths textbook solution

Answers (1)

Answer:

 Option (a)

Hint:

 \lambda is a scalar.

Given:

ax + by + cz + d = 0

Solution:

The equation of the plane through the intersection of the planes

ax + by + cz + d = 0 and lx + my + nz + p = 0

Is given by

(ax + by + cz + d) + (lx + my + nz + p) = 0, [ where \lambda is a scalar ]

x (a + l \lambda) + y (b + m \lambda) + z (c + n \lambda) + d + p \lambda = 0

Given that the required plane is parallel to the lines y = 0, z = 0, i.e., x-axes so, we have

1 (a + l \lambda) + 0 ( b + m \lambda) + 0 (c + n \lambda) = 0

a + l \lambda = 0

\lambda =-\frac{a}{l}

(a + l \lambda )x + (b + m \lambda) y + (c + n\lambda) z + (d + pλ ) = 0

\begin{aligned} &\left ( a+l\times \frac{-a}{l} \right )x +\left ( b+m\times \frac{-a}{l} \right )y+\left ( c+n\times \frac{-a}{l} \right )z+\left ( d+p\times \frac{-a}{l} \right )=0 \end{aligned}

(b l - a m) y + (c l - a n) z + d l - a p = 0

Hence, option a is correct

Posted by

Gurleen Kaur

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