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2. यदि किसी रेखा के दिक्अनुपात \( 2,6,-9 \) हैं तो उसकी दिककोज्या- |
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Answer» Direction ratios of given line are a = 2, b = 6 and c = -9 We know that the relation between Direction ratios and cosines is \(l=\frac{a}{\sqrt{a^2+b^2+c^2}},\) \(m=\frac{b}{\sqrt{a^2+b^2+c^2}},\) \(n=\frac{c}{\sqrt{a^2+b^2+c^2}}\) ∴ Direction cosines of given line are \(l=\frac{2}{\sqrt{2^2+6^2+(-9)^2}}\) \(=\frac{2}{\sqrt{4+36+81}}\)\(=\frac{2}{\sqrt{121}}\) \(=\frac{2}{11},\) \(m=\frac{6}{\sqrt{2^2+6^2+(-9)^2}}\) \(=\frac{6}{11}\) and \(n=\frac{-9}{\sqrt{2^2+6^2+(-9)^2}}\) \(=\frac{9}{11}\) Hence, direction cosines of given line are \(\frac{2}{11},\frac{6}{11}\,and\,\frac{-9}{11}.\) |
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