Find the direction cosines of the line passing through two points (1,2,4) and  (2,4,5).

1/√6, 2/√6,  1√6

We know the direction cosine of the line passing through two points P(x₁, y₁, z₁) and Q(x₂,y₂,z₂) are given by

 (x₂- x₁) /PQ , (y₂- y₁) /PQ, (z₂- z₁) /PQ

where PQ = √{ (x₂- x₁)^₂+ (y₂- y₁)² + (z₂- z₁)²} 

Here P is  (1,2,4) and Q is  (2,4,5)

So,  PQ = √{ (2-1)^₂+ (4- 2)² + (5- 4)²} = √6

Thus the direction cosines of the line joining two points is

1/√6, 2/√6, 1/√6