The distance of the point (1 ,2 ,1 ) from the line x-12= y-21= z-32 is

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Accepted Answer

Correct answer: C. (c): Given equation of line is x-12= y-21= z-32=r (say) ∴ Coordinates of any point Q on the line are (2r+1 ,r+2 ,2r+3 ). Let P be the point with coordinates (1 ,2 ,1 ). Now, d.r's of PQ are 2r+1-1 ,r+2-2 ,2r+3-1 or 2r ,r ,2r+2. Also, d.r's of the given line are 2 ,1 ,2. Since PQ is perpendicular to the given line, ∴ 4r+r+4r+4=0 ⇒9r=-4 ⇒r= -49 So, coordinates of Q arc ( 19 , 149 , 199 ). ∴ PQ= (1- 19)^2+(2- 149)^2+(1- 199)^2 = 6481+ 1681+ 10081= 1809= 2 53

$The distance of the point (1, 2, 1) from the line \frac{x - 1}{2} = \frac{y - 2}{1} = \frac{z - 3}{2} is$

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