If $\frac{1}{2}, \frac{1}{3}, n $ are direction cosines of a line, then the value of n, is

$\frac{\sqrt{23}}{6}$ $\frac{23}{6}$ $\frac{2}{3}$ $\frac{1}{6}$

$\frac{\sqrt{23}}{6}$

Since $\frac{1}{2}, \frac{1}{3}, n $ are direction cosines of a line. $∴ \frac{1}{4}+\frac{1}{9}+n^2=1 ⇒ n^2 = \frac{23}{36}⇒ n = \frac{\sqrt{23}}{6}$