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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise Fill in the blank question 19

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise Fill in the blank question 19

Answers (1)

Answer:

 3 units is the required distance.

Hint:

 use vector dot product to find the distance

Given:

 2x+y-2z-6=0 \text { and } 4x+2y-4z=0

Solution:

Let

\begin{aligned} &P_{1}\rightarrow 2x+y-2z-6=0\\ &ax+by+cz+d_{1}=0\\ &P_{2}\rightarrow 4x+2y-4z=0\\ &ax+by+cz+d_{2}=0\\ \end{aligned}

\begin{aligned} &\because P_{1}\left | \right |P_{2} \end{aligned}

\begin{aligned} &\text { Distance between } P_{1} \text { and } P_{2}=\left | \frac{d_{2}-d_{1}}{\sqrt{a^{2}+b^{2}+c^{2}}} \right |\\ &=\left | \frac{0-6}{\sqrt{2^{2}+1^{2}+(-2)^{2}}} \right |=\left | \frac{-6}{4+1+4} \right |\\ &=3\: units \end{aligned}

Posted by

Gurleen Kaur

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