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  • Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 10

Provide solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 10

Answers (1)

Answer: Correct answer is B.

Hint: \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1

Given: Lines make angle \frac{\pi}{3} \text { and } \frac{\pi}{4} \text { with } x-\text { axis and } y-\text { axis }

Solution: If a line makes angles α,β and γ with the axes then,

\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \rightarrow(1)

Hence,

\alpha=\frac{\pi}{3} \text { and } \beta=\frac{\pi}{4}

Now,

\begin{aligned} &\Rightarrow \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\\\ &\Rightarrow \cos ^{2} \frac{\pi}{3}+\cos ^{2} \frac{\pi}{4}+\cos ^{2} \gamma=1 \end{aligned}

\begin{aligned} &\Rightarrow \frac{1}{4}+\frac{1}{2}+\cos ^{2} \gamma=1 \\\\ &\Rightarrow \frac{3}{4}+\cos ^{2} \gamma=1 \end{aligned}

\begin{aligned} &\Rightarrow \cos \gamma=\frac{1}{2} \\\\ &\Rightarrow \gamma=\frac{\pi}{3} \end{aligned}

So, the correct option is (B) \frac{\pi}{3}

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