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  • Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 15

Need solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 15

Answers (1)

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Final Answer:  \frac{\sqrt{23}}{6}

Hint:

Use the property of direction cosine

Given:

Direction cosine   =\left(\frac{1}{2}, \frac{1}{3}, n\right)

To Find: 

Value of n

Solution:

By property of direction cosine, we get

\begin{aligned} &l^{2}+m^{2}+n^{2}=1 \\\\ &\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{3}\right)^{2}+n^{2}=1 \\\\ &\frac{1}{4}+\frac{1}{9}+n^{2}=1 \end{aligned}

\begin{aligned} &n^{2}=1-\frac{1}{4}-\frac{1}{9} \\ &n^{2}=\frac{23}{36} \\\\ &n=\sqrt{\frac{23}{36}} \\\\ &n=\frac{\sqrt{23}}{6} \end{aligned}
 

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