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  • Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 16 maths

Explain solution RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 16 maths

Answers (1)

Answer:

 \begin{aligned} &\lambda =-2,\lambda =1\pm \sqrt{3} \end{aligned}

Hint:

 If vectors are coplanar, their scalar triple product is zero.

\begin{aligned} &\therefore \text { For }\begin{vmatrix} \lambda &1 &2 \\ 1 &\lambda &-1 \\ 2 &-1 &\lambda \end{vmatrix}\\ &=\lambda (\lambda ^2-1)-1(\lambda +2)+2(-1-2\lambda )\\ &=\lambda ^3-\lambda -\lambda -2-2-4\lambda \\ &=\lambda ^3-6\lambda -4 \end{aligned}

Now

\begin{aligned} &\lambda ^3-6\lambda -4=0\\ &(\lambda +2)(\lambda ^2-2\lambda -2)=0\\ &\lambda =-2,\lambda =1\pm \sqrt{3} \end{aligned}

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Gurleen Kaur

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