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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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