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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26 point 1 question 1 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 1 maths textbook solution

Answers (1)

Answer: The direction cosines are 0,\frac{1}{2},\frac{\sqrt{3}}{2}

Given: Angle made by line with x, y and z-axis are 90^{\circ},60^{\circ},30^{\circ}

Hint: Find direction cosines of a line \cos \alpha ,\cos \beta ,\cos \gamma

Solution:

Let l, m and n are the direction cosines of the line and \alpha ,\beta ,\gammaare the angles made with axes.

\alpha=90 ^{\circ},\beta=60 ^{\circ},\gamma=30^{\circ}

Now,

\begin{aligned} &I=\cos \alpha \Rightarrow I=\cos 90^{\circ} \Rightarrow I=0 \\ &m=\cos \beta \Rightarrow m=\cos 60^{\circ} \Rightarrow m=\frac{1}{2} \\ &n=\cos \gamma \Rightarrow n=\cos 30^{\circ} \Rightarrow n=\frac{\sqrt{3}}{2} \end{aligned}

Therefore, the direction cosines of the line are  0,\frac{1}{2},\frac{\sqrt{3}}{2}

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