The directions of the line segment joining the points A(-1, 0, 3) and B(2, 5,1) on the line whose direction ratios are proportional to 6, 2, 3, is

$\frac{22}{7}$

The direction cosines of the line whose direction ratios are proportional to 6, 2, 3 are $\frac{6}{7}, \frac{2}{7}, \frac{3}{7}$.

∴ Projection of AB on the givenn line

$ = (2 + 1) × \frac{6}{7} + (5-0)×\frac{2}{7} + ( 1- 3) × \frac{3}{7}=\frac{22}{7}$