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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 5 Sub Question 2 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 5 Sub Question 2 Maths Textbook Solution.

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Answer :-  \lambda =\frac{-25}{8}

 Hint :- As it is given that vectors are coplanar. So use \left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ]=0  to find \lambda

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

\begin{aligned} &\vec{b}=\hat{\imath}+2 \hat{\jmath}-3 \hat{k} \\ &\vec{c}=\lambda \hat{\imath}+\lambda \hat{j}+5 \hat{k} \end{aligned}

 

As it is given vectors are coplanar

 

\left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ]=0

=\left|\begin{array}{ccc} 2 & -1 & 1 \\ 1 & 2 & -3 \\ \lambda & \lambda & 5 \end{array}\right|

\begin{aligned} =2(10+3 \lambda)+1(5+3 \lambda)+1(\lambda-2 \lambda) \end{aligned}

\begin{aligned} &=20+6 \lambda+5+3 \lambda-\lambda \\ &=8 \lambda+25 \\ &\text { As, }[\vec{a} \vec{b} \vec{c}]=0 \\ &\therefore 8 \lambda+25=0 \\ &8 \lambda=-25 \\ &\lambda=\frac{-25}{8} \end{aligned}

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