The projections of a line on the coordinate a | vedclass

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Question

(A) Let the projections of the line on the coordinate axes be $a = 4$,$b = 6$,and $c = 12$. These projections represent the direction ratios of the li

Vedclass · Accepted Answer

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

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(A) Let the projections of the line on the coordinate axes be $a = 4$,$b = 6$,and $c = 12$. These projections represent the direction ratios of the line. To find the direction cosines $(l, m, n)$,we divide each direction ratio by the magnitude of the vector $\sqrt{a^2 + b^2 + c^2}$. The magnitude is $\sqrt{4^2 + 6^2 + 12^2} = \sqrt{16 + 36 + 144} = \sqrt{196} = 14$. Thus,the direction cosines are $l = \frac{4}{14} = \frac{2}{7}$,$m = \frac{6}{14} = \frac{3}{7}$,and $n = \frac{12}{14} = \frac{6}{7}$. Therefore,the direction cosines are $(\frac{2}{7}, \frac{3}{7}, \frac{6}{7})$.

The projections of a line on the coordinate axes are $4, 6, 12$. The direction cosines of the line are

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