Show that the line through the points (1, –1, 2), (3, 4, –2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Let P (1, –1, 2), Q (3, 4, –2), R (0, 3, 2) and S (3, 5, 6) be given points.
Direction ratios of RS are 3 - 0, 5 - 3, 6 - 2 i.e. 3, 2, 4.
∴  direction cosines of RS are
        
i.e.,    
Projection of PQ on RS
                           

∴  PQ is perpendicular to RS
Hence the result.