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  • Explain Solution R.D.Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 15 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 15 Maths Textbook Solution.

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Answer :-   24 cubic units

Hint :- Use formula of volume of parallelopiped =\left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ] where, \vec{a}\: \: \vec{b}  &  \: \: \vec{c} be the adjacent edges.

Given:\begin{aligned} &2 \vec{a}=2(\hat{\imath}-\hat{\jmath}+2 \hat{k})=2 \hat{\imath}-2 \hat{\jmath}+4 \hat{k} \\ \end{aligned}

\begin{aligned} &-\vec{b}=-(3 \hat{\imath}+4 \hat{\jmath}-5 \hat{k})=-3 \hat{\imath}-4 \hat{\jmath}+5 \hat{k} \\ &3 \vec{c}=3(2 \hat{\imath}-\hat{\jmath}+3 \hat{k})=6 \hat{\imath}-3 \hat{\jmath}+9 \hat{k} \end{aligned}

∴ Volume of parallelopiped  =\mid \left [ 2\vec{a}\left ( -\vec{b} \right ) \left ( 3\vec{c} \right )\right ]\mid

=\left|\begin{array}{ccc} 2 & -2 & 4 \\ -3 & -4 & 5 \\ 6 & -3 & 9 \end{array}\right|

\begin{aligned} &=2(-36+15)+2(-27-30)+4(9+24) \\\\ &=2(-21)+2(-57)+4(33) \\\\ &=-42-114+132 \\\\ &=-24 \end{aligned}

∴ Volume of parallelopiped =\mid -24\mid =24 cubic units .

 

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