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  • Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 6

Provide solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 6

Answers (1)

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Final Answer : \frac{\pi }{2}

Hint:

Using property of direction cosine l^{2}+m^{2}+n^{2}=1

Given:

Line makes angles with y and z axes is \frac{\pi }{4}

Hence  \beta=\gamma=\frac{\pi}{4}

To Find: 

Angle made with x-axes?

Solution:

Direction cosine of a line making angle α,β,γ are

l=\cos \alpha, m=\cos \beta \text { and } n=\cos \gamma\\\\ and \; \; l^{2}+m^{2}+n^{2}=1\\\\ \Rightarrow \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1

\Rightarrow \cos ^{2} \alpha+\cos ^{2}\left(\frac{\pi}{4}\right)+\cos ^{2}\left(\frac{\pi}{4}\right)=1 \quad\left[\cos \left(\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}\right]

\begin{aligned} &\Rightarrow \cos ^{2} \alpha+\frac{1}{2}+\frac{1}{2}=1 \\\\ &\Rightarrow \cos ^{2} \alpha=1-1 \\\\ &\Rightarrow \cos ^{2} \alpha=0 \\\\ &\Rightarrow \cos \alpha=0 \end{aligned}

\Rightarrow \alpha=\frac{\pi}{2}

Therefore, the angle made by line with x -axis is \frac{\pi }{2}

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