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  • Please solve RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 13 maths textbook solution

Answers (1)

Answer:

 \begin{aligned} &=\left [ \overrightarrow{a} \quad \overrightarrow{b} \quad \overrightarrow{c} \right ] \end{aligned}

Hint:

 Simplify the expression

Given:

\begin{aligned} &(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c})\\ &=(\overrightarrow{a}+\overrightarrow{b}).\left [ \overrightarrow{b}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{b}+\overrightarrow{b}\times \overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a}+\overrightarrow{c}\times \overrightarrow{b}+\overrightarrow{c}\times \overrightarrow{c} \right ] \end{aligned}

\begin{aligned} &=(\overrightarrow{a}+\overrightarrow{b}).\left [ \overrightarrow{b}\times \overrightarrow{a}+0+\overrightarrow{b}\times \overrightarrow{c}+\overrightarrow{c}\times \overrightarrow{a}+\overrightarrow{c}\times \overrightarrow{b}+0 \right ]\\ &=(\overrightarrow{a}+\overrightarrow{b}).\left [ (\overrightarrow{b}\times \overrightarrow{a})+(\overrightarrow{c}\times \overrightarrow{a}) \right ] \end{aligned}

\begin{aligned} &=\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{a})+\overrightarrow{a}.(\overrightarrow{c}\times \overrightarrow{a})+\overrightarrow{b}.(\overrightarrow{b}\times \overrightarrow{a})+\overrightarrow{b}.(\overrightarrow{c}\times \overrightarrow{a}) \\ &=\overrightarrow{a}\overrightarrow{b}\overrightarrow{a}+\overrightarrow{a}\overrightarrow{c}\overrightarrow{a}+\overrightarrow{b}\overrightarrow{b}\overrightarrow{a}+\overrightarrow{b}\overrightarrow{c}\overrightarrow{a}\\ &=0+0+0+\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\\ &=\left [ \overrightarrow{a}\quad \overrightarrow{b}\quad \overrightarrow{c} \right ] \end{aligned}

Posted by

Gurleen Kaur

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