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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise 25 .1 Question 2 Sub Question 2 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise 25 .1 Question 2 Sub Question 2 Maths textbook Solution.

Answers (1)

Answer :- \left [ \vec{a}\:\: \vec{b}\:\: \vec{c} \right ]=12

Hint :- Use cross product & dot product

Given: \vec{a}=\hat{i}-2\hat{j}+3\hat{k}

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

       \begin{aligned} &\text { For, }[\vec{a} \vec{b} \vec{c}]=(\vec{a} \times \vec{b}) \cdot \vec{c} \\ \end{aligned}

\begin{aligned} &\vec{a} \times \vec{b}=\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 1 & -2 & 3 \\ 2 & 1 & -1 \end{array}\right| \\ \end{aligned}

            \begin{aligned} &=\hat{l}(2-3)-\hat{\jmath}(-1-6)+\hat{k}(1+4) \\ &=-\hat{\imath}+7 \hat{j}+5 \hat{k} \\ \end{aligned}

  \begin{aligned} &(\vec{a} \times \vec{b}) \cdot \vec{c}=(-\hat{\imath}+7 \hat{\jmath}+5 \hat{k}) \cdot(\hat{\jmath}+\hat{k}) \\ &=7+5 \\ &=12 \end{aligned}

\therefore \left [ \vec{a}\:\: \vec{b}\:\: \vec{c} \right ]=12

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