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KCET2019MathematicsThree Dimensional Geometry

The distance of the point ( (1,2,1) ) from the line ( x-1 2 = y-2 1 = z-3 2 ) is

Options

  1. A( 2 5 3 )
  2. B( 20 3 )
  3. C( 2 3 5 )
  4. D( 5 3 )

Correct answer

A. ( 2 5 3 )

Step-by-step solution

( x-1 2 = y-2 1 = z-3 2 = ) (x-2 d+1, y= +2, z=2 d+3 ) ( aligned P A =& [(2 +1) +( +2) +(2 +3) k )] &-[ +2 + k ] aligned ) ( [2 +(2 +2) k ] ) ( P A L ) ( P A L=0 ) ([(2 + )+(2 +2) p ] [2 + +2 k ]=0 ) ([(2 2) i +( 1) +(2 +2) 2 k ]=0 ) ([4 + +4 d+u]=0 ) (d=-4 / 9 ) (A=[2 +1, +2,2 +3] ) (A= [ 1 3 , 14 3 , 19 9 ] ) (D= (1-1 / 9)²+ ( 2+14 9 )²+ (1- 19 9 )² ) (D= (4 81 + 16 81 + 100 81 = 2 5 3 )

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