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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 11

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise very short answer type question 11

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}+\mu \overrightarrow{c}

Solution:

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

Plane passes through \overrightarrow{a} and parallel to \overrightarrow{b} & \overrightarrow{c} .

Normal vector will be ⊥ to \overrightarrow{b} & \overrightarrow{c} .

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

Putting in

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

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

Posted by

Gurleen Kaur

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