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  • Please solve RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 25 Scalar triple product exercise multiple choice question 17 maths textbook solution

Answers (1)

Answer:

 -2

Hint:

 Vectors are coplanar, then their scalar triple product is zero

\begin{aligned} &\therefore \left [ \overrightarrow{a} \quad \overrightarrow{b} \quad \overrightarrow{c} \right ]=\begin{vmatrix} 3 &-1 &2 \\ 2 &1 &3 \\ 1 &\lambda &-1 \end{vmatrix}\\ &=3(-1-3\lambda )+1(-2-3)+2(2\lambda -1)\\ &=-3-9\lambda -2-3+4\lambda -2\\ &=-5\lambda -10 \end{aligned}

As, vectors are coplanar

\begin{aligned} &\left [ \overrightarrow{a} \quad \overrightarrow{b} \quad \overrightarrow{c} \right ]=0\\ &-5\lambda -10=0\\ &\lambda =\frac{10}{-5}\\ &\lambda =-2 \end{aligned}

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