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  • Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26 point 1 question 2 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 26 Direction Cosines and Direction Ratios exercise 26.1 question 2 maths textbook solution

Answers (1)

Answer: \frac{2}{3},\frac{-1}{3},\frac{-2}{3}

Given: Direction ratios of line are (2,-1,-2)

Hint: Find direction cosines using I=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}, m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}, n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}

Solution:

Let l, m and n are the direction cosines of the line

Here (a, b, c) = (2, -1, -2) are the direction ratios of the line.

Direction cosine is related to direction ratios are

\begin{aligned} &I=\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}} \Rightarrow I=\frac{2}{\sqrt{(2)^{2}+(-1)^{2}+(-2)^{2}}} \Rightarrow \mid=\frac{2}{\sqrt{9}} \\ &m=\frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}} \Rightarrow m=\frac{c}{\sqrt{(2)^{2}+(-1)^{2}+(-2)^{2}}} \Rightarrow m=\frac{-1}{\sqrt{9}} \\ &n=\frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}} \Rightarrow n=\frac{-2}{\sqrt{(2)^{2}+(-1)^{2}+(-2)^{2}}} \Rightarrow n=\frac{-2}{\sqrt{9}} \end{aligned}

Therefore, direction cosines are  \frac{2}{3},\frac{-1}{3},\frac{-2}{3}

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