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A line with direction cosines proportion...

A line with direction cosines proportional to 2,1,2 meet each of the lines `x=y+a=z nd x+a=2y=2z`. The coordinastes of each of the points of intersection 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)`

Text Solution

Verified by Experts

The correct Answer is:
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.
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