If a line has direction ratios 2, -1, -2, determine its direction… - Vidyadip

Question

If a line has direction ratios 2, -1, -2, determine its direction cosines.

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Answer

Let the direction cosines of a line be l, m and n.

Now,

$\text{l}=\frac{2}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{2}{3}$

$\text{m}=\frac{-1}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{-1}{3}$

$\text{n}=\frac{-2}{\sqrt{2^2+(-1)^2+(-2)^2}}=\frac{-2}{3}$

$\therefore$ The direction consines of the line are $\frac{2}{3},\frac{-1}{3},\frac{-2}{3}.$

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