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  • Please Solve RD Sharma Class 12 Chapter 28 The Plane Exercise 28 .11 Question 2 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 28 The Plane Exercise 28.11 Question 2 Maths Textbook Solution.

Answers (1)

Answer:  0

Hint: Use formula  \sin \theta=\frac{\vec{b} \cdot \vec{n}}{|\vec{b}||\vec{n}|}

Given: Line is \frac{x-1}{1}=\frac{y-2}{-1}=\frac{z+1}{1}  and plane is 2 x+y-z=4

Solution: The given line is parallel to the vector  \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}} and the given plane is normal to the vector   \vec{n}=2 \hat{i}+\hat{j}-\hat{k}

We know that, the angle \theta  between the line and plane is

            \begin{aligned} &\sin \theta=\frac{(\hat{i}-\hat{j}+\hat{k}) \cdot(2 \hat{i}+\hat{j}-\hat{k})}{|\hat{i}-\hat{j}+\hat{k}||2 \hat{i}+\hat{j}-\hat{k}|} \\ & \end{aligned}                                                                    \left[\sin \theta=\frac{\vec{b} \cdot \vec{n}}{|\vec{b}||\vec{n}|}\right]

                     =\frac{2-1-1}{\sqrt{1+1+1} \sqrt{4+1+1}}=0 \\

           \Rightarrow \theta=\sin ^{-1} 0 \\

                \theta=0

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