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(A) The projections of a line on the coordinate axes are the direction ratios of the line,denoted as $a = 4$,$b = 6$,and $c = 12$.To find the directio

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$\frac{2}{7}, \frac{3}{7}, \frac{6}{7}$

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(A) The projections of a line on the coordinate axes are the direction ratios of the line,denoted as $a = 4$,$b = 6$,and $c = 12$.To find the direction cosines $(l, m, n)$,we use the formula $l = \frac{a}{\sqrt{a^2 + b^2 + c^2}}$,$m = \frac{b}{\sqrt{a^2 + b^2 + c^2}}$,and $n = \frac{c}{\sqrt{a^2 + b^2 + c^2}}$.First,calculate the magnitude: $\sqrt{4^2 + 6^2 + 12^2} = \sqrt{16 + 36 + 144} = \sqrt{196} = 14$.Now,calculate the direction cosines:$l = \frac{4}{14} = \frac{2}{7}$$m = \frac{6}{14} = \frac{3}{7}$$n = \frac{12}{14} = \frac{6}{7}$Thus,the direction cosines are $(\frac{2}{7}, \frac{3}{7}, \frac{6}{7})$.

If the projections of a line on the coordinate axes are $4, 6, 12$,what are the direction cosines of the line?

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