Question

A line with directional cosines prontional to `2, 1,2` meets each of the lines `x = y + a = z and x+ a = 2y = 2z`. The coordinates of each of the points deintersection are given by
A. `(2a,3a,a),(2a,a,a)`
B. `(3a,2a,3a),(a,a,a)`
C. `(3a,2a,3a),(a,a,2a)`
D. `(3a,3a,3a),(a,a,a)`

Answer 1

Correct Answer - B
We observe that the points `P(3a,2a,3a)` and `Q(a,a,a)` satisfy the equations of the lines `x=y+a=z` and `x+a=2y=2z` respectively. Also, direction ratios of `PQ` are proportional to `3a-a,2a-a,3a-a` i.e.`2,1,2`.
Hence option b is correct.