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  • Please solve RD Sharma class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 17 maths textbook solution

Answers (1)

Final Answer:  4

Hint:

Use the property \left[\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} y=1\right]

Given:

\alpha=\beta=\gamma

To Find: 

Number of equally inclined lines

Solution:

If α,β,γ are the angles made by line with axes, then

\begin{array}{ll} \Rightarrow \cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1 & {[\alpha=\beta=\gamma]} \end{array}

\begin{aligned} &\Rightarrow 3 \cos ^{2} \alpha=1 \\ &\Rightarrow \cos ^{2} \alpha=\frac{1}{3} \\ &\Rightarrow \cos \alpha=\cos \beta=\cos \gamma=\pm \frac{1}{\sqrt{3}} \end{aligned}

Possible direction cosine are \left(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)

Different set of direction cosine are

\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right),\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}\right),\left(\frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \text { and }\left(\frac{-1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)
 

Therefore, 4 lines are equally inclined to axes.

 

Posted by

infoexpert26

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