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  • Need solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Very Short Answer Question, question 8.

Need solution for RD Sharma Maths Class 12 Chapter 26 Directions Cosines and Direction Ratios Exercise Very Short Answer Question, question 8.

Answers (1)

Answer:

45^{\circ}

Hint:

l^{2}+m^{2}+n^{2}=1

Given:

Line makes 60^{\circ} with x-axis and y-axis.

Solution:

\begin{array}{ll} l=\cos \alpha, & \alpha \rightarrow x-\text { axis } \\ \mathrm{m}=\cos \beta, & \beta \rightarrow y-\text { axis } \\ \mathrm{n}=\cos \gamma, & \gamma \rightarrow z-\text { axis } \end{array}

We know that

\begin{aligned} &l^{2}+m^{2}+n^{2}=1 \\ &\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\ &\Rightarrow \cos ^{2} 60^{\circ}+\cos ^{2} 60^{\circ}+\cos ^{2} \gamma=1\left(\alpha=\beta=60^{\circ}\right) \\ &\Rightarrow \cos ^{2} \gamma=1-2 \cos ^{2} 60^{\circ} \\ &=1-2\left(\frac{1}{4}\right) \end{aligned}

\begin{aligned} &=1-\frac{1}{2} \\ &=\frac{1}{2} \\ &\Rightarrow \cos \gamma=\frac{1}{\sqrt{2}} \\ &\gamma=45^{\circ} \end{aligned}

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