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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 6 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 6 Maths Textbook Solution.

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Answer: \left \lceil \overrightarrow{a} \right \rceil^{2}\left \lceil \overrightarrow{b} \right \rceil^{2}

HINT :- Solve for the given vectors & simplify it.

Given: \left \lfloor (\vec{a}\: \: \vec{b} \: \: \vec{a}) \times \vec{b} \right \rfloor+(\vec{a} \cdot \vec{b})^{2}

Solution:\left \lfloor (\vec{a}\: \: \vec{b} \: \: \vec{a}) \times \vec{b} \right \rfloor+(\vec{a} \cdot \vec{b})^{2}

\begin{aligned} &=[(\vec{a} \times \vec{b}) \cdot(\vec{a} \times \vec{b})]+(\vec{a} \cdot \vec{b})^{2} \\\\ &=(\vec{a} \times \vec{b})^{2}+(\vec{a} \cdot \vec{b})^{2} \\\\ &=\left[\vec { a } | ^ { 2 } \left[\left.\vec{b}\right|^{2} \operatorname{Sin}^{2} \theta+\left[\vec { a } | ^ { 2 } \left[\left.\vec{b}\right|^{2} \cos ^{2} \theta\right.\right.\right.\right. \end{aligned}

\begin{aligned} &=\left[\left.\vec{a}\right|^{2}|\vec{b}|^{2}\left(\operatorname{Sin}^{2} \theta+\cos ^{2} \theta\right)\right. \\\\ &=\left[\left.\vec{a}\right|^{2}|\vec{b}|^{2}\right. \end{aligned}

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