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  • Please solve RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 5 maths textbook solution

Answers (1)

Answer:

 k = -8

Hint:

 If two vectors are perpendicular then their dot product is zero

  \overrightarrow{n_1}.\overrightarrow{n_2}=0

Given:

 Equation of plane x - 2y + kz = 4  and 2x + 5y - z = 9

Solution:

Equation of first plane   x - 2y + kz = 4                    … (i)

Normal vector of plane (i)  is 

\overrightarrow{n_1}=\widehat{i}-2\widehat{j}+k\widehat{k}

Equation of second plane  2x + 5y - z = 9                                 …(ii)

Normal vector of plane (ii) is

\overrightarrow{n_2}=2\widehat{i}+5\widehat{j}-\widehat{k}

(i) and (ii) are perpendicular to each other

\begin{aligned} &\Rightarrow \overrightarrow{n_1}.\overrightarrow{n_2}=0\\ &\Rightarrow (\widehat{i}-2\widehat{j}+k\widehat{k}).(2\widehat{i}+5\widehat{j}-\widehat{k})=0\\ &\Rightarrow 2-10-k\\ &\Rightarrow k = -8 \end{aligned}

Posted by

Gurleen Kaur

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