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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 5 Sub Question 1 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 5 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer:  \frac{2\pi }{3}

Hint: you must know the properly of finding angle b/w two vectors.

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

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

\begin{aligned} &(\vec{a} \cdot \vec{b})=(\hat{\imath}-\hat{\jmath}) \cdot(\hat{\jmath}+\hat{k}) \\\\ &=(0,-1+0)-1 \end{aligned}

                                    |\vec{a}|=\sqrt{(1)^{2}+(-1)^{2}+(0)^{2}} \quad=\sqrt{1+1} \quad \Rightarrow \sqrt{2}

|\vec{b}|=\sqrt{(0)^{2}+(1)^{2}+(1)^{2}} \quad=\sqrt{1+1} \quad \Rightarrow \sqrt{2}

Now we know   \vec{a}.\vec{b}=\mid \vec{a}\mid \mid \vec{b}\mid \cos \theta

\begin{aligned} &-1=(\sqrt{2})(\sqrt{2}) \cos \theta \\\\ &\frac{-1}{2}=\cos \theta \\ \end{aligned}

\begin{aligned} &\theta=\frac{2 \pi}{3} \end{aligned}

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