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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 2 Sub Question 3 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise 25.1 Question 2 Sub Question 3 Maths textbook Solution.

Answers (1)

Answer :- -30

Hint :- Use scalar triple product

Given:-  \begin{aligned} &\vec{a}=2 \hat{\imath}+3 \hat{\jmath}+\hat{k} \\ \end{aligned}

\begin{aligned} &\vec{b}=\hat{\imath}-2 \hat{\jmath}+\hat{k} \\ &\vec{c}=-3 \hat{\imath}+\hat{\jmath}+2 \hat{k} \end{aligned}

We Know ,[\vec{a} \vec{b} \vec{c}]=(\vec{a} \times \vec{b}) \cdot \vec{c}

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

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

Now \begin{aligned} &{[\vec{a} \times \vec{b}] \cdot \vec{c}=[5 \hat{\imath}-\hat{\jmath}-7 \hat{k}) \cdot[-3 \hat{\imath}+\hat{\jmath}+2 \hat{k}]} \\\\ \end{aligned}

                          \begin{aligned} &\quad=-15-1-14 \\\ \end{aligned}

                           \begin{aligned} &=-30 \end{aligned}

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