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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 22

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 22

Answers (1)

Answer:

 Option (d)

Hint:

 Find the angle with vector dot product.

Given:

 \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}

Solution:

Given line

\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}

is parallel to the vector

\overrightarrow{b}=3\widehat{i}+4\widehat{j}+5\widehat{k}

Equation to the plane is 

2x - 2y + z = 5

Normal to the plane is

\overrightarrow{n}=2\widehat{i}-2\widehat{j}+\widehat{k}

If angle between line and plane is \theta

Then

\begin{aligned} &sin\theta =\frac{\left | \overrightarrow{b}.\overrightarrow{n} \right |}{\left | \overrightarrow{b} \right |.\left | \overrightarrow{n} \right |}\\ &=\frac{\left | (3\widehat{i}+4\widehat{j}+5\widehat{k}).(2\widehat{i}-2\widehat{j}+\widehat{k}) \right |}{\sqrt{3^2+4^2+5^2.\sqrt{4+4+1}}}\\ &=\frac{\left | 6-8+5 \right |}{\sqrt{50}.\sqrt{9}}\\ &=\frac{3}{15\sqrt{3}}\\ &=\frac{1}{5\sqrt{3}}\\ &\therefore sin\theta =\frac{\sqrt{2}}{10} \end{aligned}

Posted by

Gurleen Kaur

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