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  • If a line has the direction ratios –18, 12, – 4, then what are its direction cosines ?

3.  If a line has the direction ratios –18, 12, – 4, then what are its direction cosines ?

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GIven a line has direction ratios of -18, 12, – 4 then its direction cosines are;

Line having direction ratio -18 has direction cosine: 

\frac{-18}{\sqrt{(-18)^2+(12)^2+(-4)^2}} = \frac{-18}{22} = \frac{-9}{11}

Line having direction ratio 12 has direction cosine:

\frac{12}{\sqrt{(-18)^2+(12)^2+(-4)^2}} = \frac{12}{22} =\frac{6}{11}

Line having direction ratio -4 has direction cosine:

\frac{12}{\sqrt{(-4)^2+(12)^2+(-4)^2}} = \frac{-4}{22} = \frac{-2}{11}

Thus, the direction cosines are \frac{-9}{11},\ \frac{6}{11},\ \frac{-2}{11}.

 

Posted by

Divya Prakash Singh

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