A line through the points A(3, 4, 1) and B(5, 1, 6) is drawn.

Directions cosines of the line passing through the points A and B are :

$\frac{2}{\sqrt{38}},-\frac{3}{\sqrt{38}},\frac{5}{\sqrt{38}}$

Direction ratios of AB → $(5-3,1-4,6-1)$

$=(2,-3,5)$

Direction cosines $\left(\frac{2}{\sqrt{2^2+3^2+5^2}},\frac{-3}{\sqrt{2^2+3^2+5^2}},\frac{5}{\sqrt{2^2+3^2+5^2}}\right)$

$=\left(\frac{2}{\sqrt{38}},-\frac{3}{\sqrt{38}},\frac{5}{\sqrt{38}}\right)$