Question

If a line passes through two points (1,2,3) & (4,5,6) then the direction ratios of that line would be -

• A. 1, 2, 3
• B. 3, 2, 1
• C. 3, 3, 3
• D. 3, 4, 5

Answer 1

The correct option is C 3, 3, 3

Let’s solve this question with the help of vectors. Let ‘P’ be the point having coordinates (1,2,3) and Q be the point having coordinates as (4,5,6).
So position vector OP ‘O’ being origin will be = 1i + 2j + 3k
And the position vector OQ will be = 4i + 5j + 6k
Thus the vector PQ can be given by (4i + 5j + 6k) - (1i + 2j + 3k) = 3i + 3j + 3k
This vector represents the line segment PQ.
We know that if a vector is ai+ bj + ck, then its direction ratios are a,b,c. Similarly here, the direction ratios will be 3, 3, 3 .