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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 15

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 15

Answers (1)

Answer:

 \overrightarrow{r}=\overrightarrow{a}+\left ( \frac{\overrightarrow{a}-\overrightarrow{n}}{\overrightarrow{b}-\overrightarrow{n}} \right ).\overrightarrow{b}

Hint:

 Put Eqn (i) in Eqn (ii)

Given:

 \overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b} \text { meets the plane }\overrightarrow{r}.\overrightarrow{n}=0

Solution:

\begin{aligned} &\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b} \qquad \qquad \dots(i)\\ &\overrightarrow{r}.\overrightarrow{n}=0 \qquad \qquad \dots(ii) \end{aligned}

Put (i) in(ii).

\begin{aligned} &(\overrightarrow{a}+\lambda \overrightarrow{b}).\overrightarrow{n}=0\\ &\Rightarrow \overrightarrow{a}.\overrightarrow{n}+\lambda \overrightarrow{b}.\overrightarrow{n}=0\\ &\Rightarrow \lambda \overrightarrow{b}.\overrightarrow{n}=-\overrightarrow{a}.\overrightarrow{n}\\ &\Rightarrow \lambda =-\frac{\overrightarrow{a}.\overrightarrow{n}}{\overrightarrow{b}.\overrightarrow{n}} \end{aligned}

Putting the value of λ in eqn (i), we get

\vec{r}=\vec{a}-(\frac{\vec{a}\cdot\vec{n}}{\vec{b}\cdot\vec{n}})\vec{b}

Posted by

Gurleen Kaur

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