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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise Fill In The Blanks Question 9 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product  Exercise Fill In The Blanks Question 9 Maths Textbook Solution.

Answers (1)

Answer: 0

HINT :- Use formula of volume of parallelepiped =\left [ \overrightarrow{a}\: \overrightarrow{b}\: \overrightarrow{c} \right ]

Given:  Adjacent edges

\overrightarrow{a}-\overrightarrow{b}\overrightarrow{b}-\overrightarrow{c} & \overrightarrow{c}-\overrightarrow{a},where \overrightarrow{a},\overrightarrow{b}&\overrightarrow{c}are adjacent edges.

Solution:

∴  volume of parallelopied     

=[\vec{a}-\vec{b}\hspace{0.2cm}\vec{b}-\vec{c}\hspace{0.2cm} \vec{c}-\vec{a}]

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

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

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

 

\left ( \therefore \vec{a}.\left ( \vec{b}\times \vec{c} \right )=\vec{b}.\left ( \vec{c}\times \vec{a} \right )=\left [ \vec{a}\vec{b}\vec{c} \right ] \right )

=0

Posted by

infoexpert21

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