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  • Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 1 sub question 3 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 1 sub question 3 maths textbook solution

Answers (1)

Answer:

              \cos ^{-1}\left ( -\frac{16}{21} \right )

Hint:

              \cos \theta=\frac{\overrightarrow{n_{1}} \cdot \overrightarrow{n_{2}}}{\left|\overrightarrow{n_{1}}\right|\left|\overrightarrow{n_{2}}\right|}

Given:

              \vec{r} \cdot(2 \hat{\boldsymbol{\imath}}+3 \hat{\boldsymbol{\jmath}}-6 \hat{\boldsymbol{k}})=\mathbf{5} \text { And } \vec{r} \cdot(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})=9

Solution:

\begin{aligned} &\vec{n}_{1}=2 \hat{\imath}+3 \hat{\jmath}-6 \hat{k} \\ &\vec{n}_{2}=\hat{\imath}-2 \hat{\jmath}+2 \hat{k} \\ &\cos \theta=\frac{\vec{n}_{1} \cdot \vec{n}_{2}}{\left|\vec{n}_{1}\right| \cdot\left|\vec{n}_{2}\right|}=\frac{(2 \hat{\imath}+3 \hat{\jmath}-6 \hat{k}) \cdot(\hat{\imath}-2 \hat{\jmath}+2 \hat{k})}{|2 \hat{\imath}+3 \hat{\jmath}-6 \hat{k}| \cdot|\hat{\imath}-2 \hat{\jmath}+2 \hat{k}|} \\ &=\frac{2-6-12}{\sqrt{4+9+36} \cdot \sqrt{1+4+4}}=\frac{-16}{3 \times 7} \\ &=-\frac{16}{21} \\ &\theta=\cos ^{-1}\left(-\frac{16}{21}\right) \end{aligned}

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