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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 7 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product  Exercise Fill In The Blanks Question 7 Maths Textbook Solution.

Answers (1)

Answer:  \pm 12

HINT :- Simplify the given value.

Given: Volume of parallelopiped =6 cubic units

Solution:         

We need to find,

\left \lceil \overrightarrow{a}+\overrightarrow{b}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{c}+\overrightarrow{a} \right \rceil

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

(using scalar triple product)

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

=(\vec{a}+\vec{b}) \cdot[(\vec{b} \times \vec{c})+(\vec{b} \times \vec{a})+0+(\vec{c} \times \vec{a})]

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

              +\vec{b} \cdot(\vec{b} \times \vec{c})+\vec{b} \cdot(\vec{b} \times \vec{a})+\vec{b} \cdot\left(\vec{c} \times\overrightarrow{a}\right)

we Know \overrightarrow{a}.\left ( \overrightarrow{b}\times \overrightarrow{a} \right )=0

=\left \lceil \overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \right \rceil+0+0+0+0+\left \lceil \overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \right \rceil

=2\left \lceil \overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \right \rceil

Now, value of volume of parallelopiped  =6

=\pm \left \lceil \overrightarrow{a}\overrightarrow{b}\overrightarrow{c} \right \rceil=6

Substituting values we get

=\pm 2\left ( 6 \right )

=\pm 12

 

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