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  • Need solution for RD Sharma maths class 12 chapter 25 Scalar triple product exercise multiple choice question 15

Need solution for RD Sharma maths class 12 chapter 25 Scalar triple product exercise multiple choice question 15

Answers (1)

Answer:

 =3\left [ \overrightarrow{a} \quad \overrightarrow{b}\quad \overrightarrow{c} \right ]

Hint:

 Just simplify the expression

Given:

\begin{aligned} &=(\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c}).\left \{ (\overrightarrow{a}-\overrightarrow{b})\times (\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}) \right \}\\ &=(\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c}).\left \{ \overrightarrow{a}\times \overrightarrow{a}-\overrightarrow{a}\times \overrightarrow{b}-\overrightarrow{a}\times \overrightarrow{c}-\overrightarrow{b}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{b}+\overrightarrow{b}\times \overrightarrow{c} \right \}\\ &=(\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c}).(-\overrightarrow{a}\times \overrightarrow{c}+\overrightarrow{b}\times \overrightarrow{c})\\ & =\left [ \overrightarrow{a} \quad \overrightarrow{b}\quad \overrightarrow{c} \right ]+2\left [ \overrightarrow{a} \quad \overrightarrow{b}\quad \overrightarrow{c} \right ]\\ &=3\left [ \overrightarrow{a} \quad \overrightarrow{b}\quad \overrightarrow{c} \right ] \end{aligned}

Posted by

Gurleen Kaur

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