If the direction ratios of a line are 1, 1, 2 | vedclass

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(A) The direction cosines $(l, m, n)$ are given by the formulas: $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}, m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}, n = \fra

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$\pm(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}})$

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(A) The direction cosines $(l, m, n)$ are given by the formulas: $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}, m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}, n = \frac{c}{\sqrt{a^2 + b^2 + c^2}}$ Here,the direction ratios are $a = 1, b = 1, c = 2$. First,calculate the magnitude: $\sqrt{a^2 + b^2 + c^2} = \sqrt{1^2 + 1^2 + 2^2} = \sqrt{1 + 1 + 4} = \sqrt{6}$. Substituting these values,we get: $l = \frac{1}{\sqrt{6}}, m = \frac{1}{\sqrt{6}}, n = \frac{2}{\sqrt{6}}$. Since direction cosines can be positive or negative depending on the direction of the line,the direction cosines are $\pm(\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}})$.

If the direction ratios of a line are $1, 1, 2$,find the direction cosines of the line.

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