If lines `x=y=za n dx=y/2=z/3` and third line passing through `(1,1,1)` form a triangle of area `sqrt(6)` units, then the point of intersection of third line with the second line will be a. `(1,2,3)` b. `2,4,6` c. `4/3,6/3,(12)/3` d. none of these

Options

A. (1,2,3)
B. (2,4,6)
C. `((4)/(3),(8)/(3),(12)/(3))`
D. none of these

Answer

b

Explanation

Let any point on the second line be `(lamda,2lamda,3lamda)`

`costheta=(6)/(sqrt42),sintheta=(sqrt6)/(sqrt42)`
`Delta_(OAB)=(1)/(2)(OA)OBsintheta`
`=(1)/(2)sqrt(3)lamdasqrt14xxsqrt(6)/sqrt(42)=sqrt(6)`
or `lamda=2`
So B is (2,4,6)