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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 3 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 5 Sub Question 3 Maths Textbook Solution.

Answers (1)

Answer:\lambda =6

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}+2 \hat{\jmath}-3 \hat{k} \\ \end{aligned}

\begin{aligned} &\vec{b}=3 \hat{\imath}+\lambda \hat{\jmath}+\hat{k} \\ &\vec{c}=\hat{\imath}+2 \hat{\jmath}+2 \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} &=\left|\begin{array}{ccc} 1 & 2 & -3 \\ 3 & \lambda & 1 \\ 1 & 2 & 2 \end{array}\right| \\ &=1(2 \lambda-2)-2(6-1)-3(6-\lambda) \\ &=2 \lambda-2-10-18+3 \lambda \\ &=5 \lambda-30 \end{aligned}

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

\therefore 5\lambda -30=0

5\lambda =30

\lambda =6

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