class 12 maths three dimensional geometry

If a line has direction ratios $- 18,12, - 4$ then what are its direction cosines ?

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📘 Three Dimensional Geometry NCERT,EX.11.1,Q.3, Page .467 SA

If a line has direction ratios $- 18,12, - 4$ then what are its direction cosines ?

Official Solution

VVidaara Team ✓ Verified solution NCERT & Exemplar

The given direction ratios are $< - 18,12, - 4 >$

As $\sqrt {{{( - 18)}^2} + {{(12)}^2} + {{( - 4)}^2}} = \sqrt {484} = 22,$

therefore , direction cosines of the line are
$< \cfrac{{ - 18}}{{22}},\cfrac{{12}}{{22}}, - \cfrac{4}{{22}} >$ i.e., $< - \cfrac{9}{{11}},\cfrac{6}{{11}},\cfrac{{ - 2}}{{11}} >$

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