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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 4 Maths Textbook Solution.

Provide Solution For R.D. Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 4 Maths Textbook Solution.

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Answer: 0

HINT :- Simplify the expression

Given: \vec{a} \cdot\{(\vec{b}+\vec{c}) \times(\vec{a}+\vec{b}+\vec{c})\}

Solution:\vec{a} \cdot\{(\vec{b}+\vec{c}) \times(\vec{a}+\vec{b}+\vec{c})\}

\begin{aligned} &=\vec{a} \cdot\{(\vec{b} \times \vec{a})+(\vec{b} \times \vec{b})+(\vec{b} \times \vec{c})+(\vec{c} \times \vec{a})+(\vec{c} \times \vec{b})+(\vec{c}\times \vec{c})\} \\\\ &=\vec{a} \cdot\left\{(\vec{b} \times \vec{a})+0+(\vec{b} \times \vec{c})+\left(\vec{c} \times \vec{a}\right)+(\vec{c} \times \vec{b})+0\right\} \end{aligned}

\begin{aligned} &=\vec{a} \cdot(\vec{b} \times \vec{a})+\vec{a} \cdot(\vec{b} \times \vec{c})+\vec{a} \cdot(\vec{c} \times \vec{a})+\vec{a} \cdot(\vec{c} \times \vec{b}) \\ \end{aligned}

\begin{aligned} &=0+[ \vec{a}\hspace{0.2cm} \vec{b}\hspace{0.2cm} \vec{c}]+0+[ \vec{a} \hspace{0.2cm}\hspace{0.2cm}\vec{c} \hspace{0.2cm}\vec{b}] \\\\ &=[ \vec{a} \hspace{0.2cm}\vec{b}\hspace{0.2cm} \vec{c}]+[\vec{a}\hspace{0.2cm} \vec{c}\hspace{0.2cm} \vec{b}] \\\\ &=(\therefore [ \vec{a}\hspace{0.2cm} \vec{b}\hspace{0.2cm} \vec{c}]=-[ \vec{a}\hspace{0.2cm} \vec{c}\hspace{0.2cm} \vec{b}] \end{aligned}

=0

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