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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 4 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products  Exercise 23.1 Question 4 Maths Textbook Solution.

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Answer: - 9

Hint: you must know the rules of solving vectors.

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

Solution:  \vec{a}=\hat{i}-\hat{j} and \vec{b}=-\hat{j}+2\hat{k}

Find \left ( \vec{a}-2\vec{b} \right ).\left ( \vec{a}+\vec{b} \right )

\begin{aligned} &(\vec{a}-2 \vec{b})=(\hat{\imath}-\hat{\jmath})-2(-\hat{\jmath}+2 \hat{k}) \\\\ &=(\hat{\imath}-\hat{\jmath}+2 \hat{\jmath}-4 \hat{k}) \\\\ &(\vec{a}+\vec{b})=(\hat{\imath}-\hat{\jmath})+(-\hat{\jmath}+2 \hat{k}) \\ \end{aligned}

\begin{aligned} &=\hat{\imath}-\hat{\jmath}-\hat{\jmath}+2 \hat{k} \\\\ &=\hat{\imath}-2 \hat{\jmath}+2 \hat{k} \\\\ &(\vec{a}-2 \vec{b}) \cdot(\vec{a}+\vec{b}) \\\\ &\Rightarrow(\hat{\imath}+\hat{\jmath}-4 \hat{k})(\hat{\imath}-2 \hat{\jmath}+2 \hat{k}) \\\\ &\Rightarrow 1-2-8 \\\\ &\Rightarrow-9 \end{aligned}

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