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  • Provide solution for RD Sharma maths class 12 chapter 25 Scalar triple product exercise multiple choice question 10

Provide solution for RD Sharma maths class 12 chapter 25 Scalar triple product exercise multiple choice question 10

Answers (1)

Answer:

 =\left | \overrightarrow{a} \right |^2\left | \overrightarrow{b} \right |^2

Hint:

 Simplify expression

Given:

\begin{aligned} &\left [ \overrightarrow{a} \quad \overrightarrow{b} \quad \overrightarrow{a}\times \overrightarrow{b} \right ]+\left [ \overrightarrow{a}. \overrightarrow{b} \right ]^2\\ &=(\overrightarrow{a}\times \overrightarrow{b}).(\overrightarrow{a}\times \overrightarrow{b})+\left [ \overrightarrow{a}. \overrightarrow{b} \right ]^2\\ &=(\overrightarrow{a}\times \overrightarrow{b})^2+\left [ \overrightarrow{a}. \overrightarrow{b} \right ]^2\\ &=\left | \overrightarrow{a} \right |^2\left | \overrightarrow{b} \right |^2sin^2\theta +\left | \overrightarrow{a} \right |^2\left | \overrightarrow{b} \right |^2cos^2\theta\\ &=\left | \overrightarrow{a} \right |^2\left | \overrightarrow{b} \right |^2(sin^2\theta+cos^2\theta )\\ &=\left | \overrightarrow{a} \right |^2\left | \overrightarrow{b} \right |^2 \end{aligned}

Posted by

Gurleen Kaur

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