Question

if a line has the direction ratios _18,12 _4, then what are its direction cosines
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Answer 1

The direction cosines of the line with direction ratios -18,12 and -4 are $\frac{-9}{11}$ , $\frac{6}{11}$ and $\frac{-2}{11}$.

Above question is a bit misplaced and the correct question is

Q.  If a line has the direction ratios -18,12, -4, then what are its direction cosines.

Solution:

• If the line has direction ratios a,b,c then the direction cosines of the line is calculated by $\frac{a}{\sqrt{a^2+b^2+c^2} }$ , $\frac{b}{\sqrt{a^2+b^2+c^2} }$ and $\frac{c}{\sqrt{a^2+b^2+c^2} }$.

• Given direction ratios are -18, 12 and -4 then the direction cosines will be,

• $\frac{-18}{\sqrt{{(-18)}^2+12^2+{(-4)}^2} }$ , $\frac{12}{\sqrt{{(-18)}^2+12^2+{(-4)}^2} }$ and $\frac{-4}{\sqrt{{(-18)}^2+12^2+{(-4)}^2} }$.

• $\frac{-18}{\sqrt{484} }$ , $\frac{12}{\sqrt{484 }}$ and $\frac{-4}{\sqrt{484}}$.

• $\frac{-18}{22}$ , $\frac{12}{22}$ and $\frac{-4}{22}$.

• $\frac{-9}{11}$ , $\frac{6}{11}$ and $\frac{-2}{11}$.

• The direction cosines of the line are $\frac{-9}{11}$ , $\frac{6}{11}$ and $\frac{-2}{11}$.