If a line has the direction ratios 4, −12, 18, then find its dire… - Vidyadip

Question

If $a$ line has the direction ratios $4, −12, 18,$ then find its direction cosines

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Answer

Direction ratios of the line are $a=4, b=-12, c=18$.
Let $I , m , n$ be the direction cosines of the line.
Then $\mid=\frac{a}{\sqrt{a^2+b^2+c^2}}$
$=\frac{4}{\sqrt{4^2+(-12)^2+(18)^2}}$
$=\frac{4}{\sqrt{16+144+324}}$
$=\frac{4}{22}$
$=\frac{2}{11}$
$m=\frac{b}{\sqrt{a^2+b^2+c^2}}$
$=\frac{-12}{\sqrt{4^2+(-12)^2+(18)^2}}$
$=\frac{-12}{\sqrt{16+144+324}}$
$=\frac{-12}{22}$
$=\frac{-6}{11}$
and
$ n=\frac{c}{\sqrt{a^2+b^2+c^2}}$
$=\frac{18}{\sqrt{4^2+(-12)^2+(18)^2}}$
$=\frac{18}{\sqrt{16+144+324}}$
$=\frac{18}{22}$
$=\frac{9}{11} $
Hence, the direction cosines of the line are $\frac{2}{11}, \frac{-6}{11}, \frac{9}{11}$.

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