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  • Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product Exercise 25.1 Question 2 Sub Question 1 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 25 Scalar Triple Product  Exercise 25.1 Question 2 Sub Question 1  Maths textbook Solution.

Answers (1)

Answer: 4

Hint :- Use cross product & dot product

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

\vec{b}=\hat{i}+\hat{j}-\hat{k}

\vec{b}=3\hat{i}-\hat{k}

We Know \left [ \vec{a}\vec{b}\vec{c} \right ]=\left ( \vec{a}\times \vec{b} \right ).\vec{c}

\begin{aligned} &\therefore \vec{a} \times \vec{b}=\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & -3 & 0 \\ 1 & 1 & -1 \end{array}\right| \\\\ &=\hat{i}(3-0)-\hat{\jmath}(-2-0)+\hat{k}(2+3) \\\\ &=3 \hat{\imath}+2 \hat{\jmath}+5 \hat{k} \\ \end{aligned}

\begin{aligned} &\text { Now, }(\vec{a} \times \vec{b}) \cdot \vec{c}=(3 \hat{i}+2 \hat{\jmath}+5 \hat{k}) \cdot(3 \hat{i}+0 \hat{j}-\hat{k}) \\\\ &=9+0-5 \\\\ &=4 \end{aligned}

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