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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 2 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise Fill In The Blanks Question 2 Maths textbook Solution.

Answers (1)

Answer: 20

Hint :- Solve the given expression & simplify it.

\begin{aligned} &[\vec{a}\ \vec{b}\ \vec{c}]=10 \\ &\vec{a} \cdot\left(\vec{b} \times \vec{c}\right)=10 \end{aligned}

or

(\vec{a}\times\vec{b})\cdot\vec{c}=10

or

\begin{aligned} &\vec{b} \cdot(\vec{c} \times \vec{a})=10 \\ \end{aligned}

Solution:

\begin{aligned} &{[\vec{a}+\vec{b} \: \: \vec{b}+\vec{c}\: \: \vec{c}+\vec{a}]} \end{aligned}

=(\vec{b}+\vec{b}) \cdot\left[(\vec{b}+\vec{c}) \times\left(\vec{c}+\vec{a}\right)\right]

=\left ( \vec{a}+\vec{b} \right ).\left \lceil \left ( \vec{b} \times \vec{c}\right )+\left ( \vec{b}\times \vec{a} \right )+\left ( \vec{c}\times \vec{c} \right )+\left ( \vec{c}\times \vec{a} \right ) \right \rceil

=\left ( \vec{a}+\vec{b} \right ).\left \lceil \left ( \vec{b} \times \vec{c}\right )+\left ( \vec{b}\times \vec{a} \right )+\left ( \vec{c}\times \vec{a} \right ) \right \rceil

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

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

 

=10+10

=20

 

 

Posted by

infoexpert21

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