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  • Please solve RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 21 maths textbook solution

Please solve RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 21 maths textbook solution

Answers (1)

Answer:

 \left \{ \overrightarrow{r}-(a\widehat{i}+b\widehat{j}+c\widehat{k}) \right \}(\widehat{i}+\widehat{j}+\widehat{k})=0

Hint:

 we will use equation of plane as

\overrightarrow{r}.\overrightarrow{n}=\overrightarrow{d}

Given:

 Plane passing through (a,b,c) and parallel to plane

\overrightarrow{r}.(\widehat{i}+\widehat{j}+\widehat{k})=2

Solution:

\overrightarrow{r}.(\widehat{i}+\widehat{j}+\widehat{k})=2 \qquad \qquad \dots(i)

So the vector, normal to the plane is

\overrightarrow{n}=\widehat{i}+\widehat{j}+\widehat{k}

∴Eqn. of plane to (i) is

\overrightarrow{r}.\overrightarrow{n}=\overrightarrow{d}

\Rightarrow \overrightarrow{r}.(\widehat{i}+\widehat{j}+\widehat{k})=\overrightarrow{d} \qquad \qquad \dots(ii)

Plane (ii) passing through (a,b,c)

\Rightarrow (a\widehat{i}+b\widehat{j}+c\widehat{k}) .(\widehat{i}+\widehat{j}+\widehat{k})=\overrightarrow{d} \qquad \qquad \dots(iii)

Putting (iii) in (ii), we get

\begin{aligned} &\Rightarrow \overrightarrow{r}.(\widehat{i}+\widehat{j}+\widehat{k})=(a\widehat{i}+b\widehat{j}+c\widehat{k}).(\widehat{i}+\widehat{j}+\widehat{k})\\ \end{aligned}

\Rightarrow \left \{ \overrightarrow{r}-(a\widehat{i}+b\widehat{j}+c\widehat{k}) \right \}(\widehat{i}+\widehat{j}+\widehat{k})=0

Posted by

Gurleen Kaur

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