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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 1 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 5 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer :-  \lambda =1

 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}=\hat{\imath}+\hat{k}-\hat{\jmath} \\ \end{aligned}

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

As it is mentioned that vectors are coplanar it means that \left [ \vec{a}\: \: \vec{b}\: \: \vec{c} \right ]=0

\begin{aligned} &\therefore\left|\begin{array}{ccc} 1 & -1 & 1 \\ 2 & 1 & -1 \\ \lambda & -1 & \lambda \end{array}\right| \\ \end{aligned}

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

\begin{aligned} &\text { As, }[\vec{a} \vec{b} \vec{c}]=0 \\ &\therefore 3 \lambda-3=0 \\ &3 \lambda=3 \\ &\lambda=1 \end{aligned}

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