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  • Explain solution RD Sharma Class 12 Chapter 26 Direction Cosines and Direction Ratios Exercise Very Short Answer Question, question 21 Maths.

Explain solution RD Sharma Class 12 Chapter 26 Direction Cosines and Direction Ratios Exercise Very Short Answer Question, question 21 Maths.

Answers (1)

Answer:

30^{\circ}

Hint:

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

Given:

Lines makes 90^{\circ} and 60^{\circ} with x-axis and y-axis.

Solution:

Here

\alpha =90^{\circ}

\beta =60^{\circ}

We know that

\begin{aligned} &\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 \\ &\Rightarrow \cos ^{2} 90^{\circ}+\cos ^{2} 60^{\circ}+\cos ^{2} \gamma=1 \\ &\Rightarrow 0+\left(\frac{1}{2}\right)^{2}+\cos ^{2} \gamma=1 \\ &\Rightarrow \cos ^{2} \gamma=1-\frac{1}{4} \\ &=\frac{3}{4} \\ &\cos \gamma=\frac{\sqrt{3}}{2} \mid \\ &\gamma=30^{\circ} \end{aligned}

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