Question

If a line has the direction ratio $18,12,4$, then its direction cosines are:

• A. $\frac{9}{11}$, $\frac{6}{11}$, $\frac{2}{11}$
• B. $\frac{9}{13}$, $\frac{6}{13}$, $\frac{2}{13}$
• C. $\frac{9}{7}$, $\frac{6}{7}$, $\frac{2}{7}$
• D. None of these

Answer 1

The correct option is A $\frac{9}{11}$, $\frac{6}{11}$, $\frac{2}{11}$

Dr's of the line are : 18, 12, 4

Dc's = $\frac{18}{\sqrt{{18}^2+{12}^2+4^2}},\frac{12}{\sqrt{{18}^2+{12}^2+4^2}},\frac{4}{\sqrt{{18}^2+{12}^2+4^2}}$

$=\frac{18}{22},\frac{12}{22},\frac{4}{22}$

$=\frac{9}{11},\frac{6}{11},\frac{2}{11}$