The distance of the point (1, 0, 2) from the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/(12)` and the plane x y + z = 16, is : (1) `2sqrt(14)` (2) 8 (3) `3sqrt(21)` (4) 27

Explanation

`(x-2)/3 = (y+1)/4 = (z-2)/12 = lamda`

`x= 3 lamba + 2; y= 4 lamda - 1; z= 12 lamda + 2`

`(x,y,z) -> x-y+z=16`

`3 lamda + 2 - ( 4 lamda - 1) + 12 lamda + 2 = 16`

`3 lamda + 2 - 4 lamda + 1 + 12 lamda + 2 = 16`

`11 lamda = 11`

`lamda = 1`

`(x,y,z) = (5,3,14)`

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