1.

Thedistance 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

Answer» `(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)`
`(1,0,2) & (5,3,14)`
`d= sqrt((5-1)^2 + (3-0)^2 + (14-2)^2)`
`= sqrt(16 + 9 + 144) = sqrt(169) = 13`
option 3 is correctAnswer


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