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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 14

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 14

Answers (1)

Answer:

 (\overrightarrow{r}-\overrightarrow{a}).(\overrightarrow{b}\times \overrightarrow{c})

Hint:

 Equation of plane in scalar product form

(\overrightarrow{r}-\overrightarrow{a}).\overrightarrow{n}=0

Given:

 \overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b} \text { and }\overrightarrow{r}=\overrightarrow{a}+\mu \overrightarrow{c}

Solution:

\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b} \text { and }\overrightarrow{r}=\overrightarrow{a}+\mu \overrightarrow{c}

Plane will pass through \overrightarrow{a}.

 Normal of plane will be ⊥ to be both \overrightarrow{b}& \overrightarrow{c}

\overrightarrow{n}=\overrightarrow{b}\times \overrightarrow{c}

∴ General Eqn of the plane

(\overrightarrow{r}-\overrightarrow{a}).\overrightarrow{n}=0

\Rightarrow (\overrightarrow{r}-\overrightarrow{a}).(\overrightarrow{b}\times \overrightarrow{c})=0

Posted by

Gurleen Kaur

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