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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 22

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 22

Answers (1)

Answer:

 \overrightarrow{r}.(2\widehat{i}-3\widehat{j}+6\widehat{k})=35

Hint:

 we will use equation of plane as

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

Given:

 Normal vector of plane is

2\widehat{i}-3\widehat{j}+6\widehat{k}

Solution:

\overrightarrow{n}=2\widehat{i}-3\widehat{j}+6\widehat{k}

and distance from the origin =5 units

We know that

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

\begin{aligned} &\Rightarrow \overrightarrow{r}.\frac{(2\widehat{i}-3\widehat{j}+6\widehat{k})}{\sqrt{4+9+36}}=5\\ &\Rightarrow \overrightarrow{r}.(2\widehat{i}-3\widehat{j}+6\widehat{k})=5\times \sqrt{49}\\ &\Rightarrow \overrightarrow{r}.(2\widehat{i}-3\widehat{j}+6\widehat{k})=5\times 7\\ &\Rightarrow \overrightarrow{r}.(2\widehat{i}-3\widehat{j}+6\widehat{k})=35 \end{aligned}

Posted by

Gurleen Kaur

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