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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 5 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 5 Maths Textbook Solution.

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Answer: 0

HINT :- Just simplify using scalar triple product

Given: [ \overrightarrow{a} -\overrightarrow{b}\overrightarrow{b}-\overrightarrow{c}\overrightarrow{c}-\overrightarrow{a}]

 

Solution:[ \overrightarrow{a} -\overrightarrow{b}\overrightarrow{b}-\overrightarrow{c}\overrightarrow{c}-\overrightarrow{a}]

=\left ( \overrightarrow{a}-\vec{b} \right ).\left \{ \left ( \overrightarrow{b}- \overrightarrow{c} \right ) \times \left ( \overrightarrow{c}-\overrightarrow{a} \right )\right \}

=\left ( \overrightarrow{a}-\vec{b} \right ).\left \{ \left ( \overrightarrow{b}\times \overrightarrow{c} \right ) - \left ( \overrightarrow{b}\times \overrightarrow{a} \right )-\left ( \overrightarrow{c}\times\overrightarrow{c} \right )+\left ( \overrightarrow{c}\times \overrightarrow{a} \right )\right \}

=\left ( \overrightarrow{a}-\vec{b} \right ).\left \{ \left ( \overrightarrow{b}\times \overrightarrow{c} \right ) - \left ( \overrightarrow{b}\times \overrightarrow{a} \right )+\left ( \overrightarrow{c}\times \overrightarrow{a} \right )\right \}

=\overrightarrow{a}.\left ( \overrightarrow{b}\times \vec{c} \right )-\overrightarrow{a}.\left ( \vec{b}\times \vec{a} \right )+\vec{a}.\left ( \vec{c}\times \vec{a} \right )

                                            =-\overrightarrow{b}.\left ( \overrightarrow{b}\times \vec{c} \right )+\overrightarrow{b}.\left ( \vec{b}\times \vec{a} \right )-\vec{b}.\left ( \vec{c}\times \vec{a} \right )

 

=0

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