Find the direction cosines of the line passing through two points (1,2,4) and (2,4,5).
Answer & explanation
Correct answer: option 4
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