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Three Dimensional Geometry

Question
CBSEENMA12036235

The distance between the line straight r with rightwards arrow on top space equals space 2 straight i with hat on top space minus 2 straight j with hat on top space plus 3 straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top minus straight j with hat on top space plus 4 straight k with hat on top right parenthesis and the plane straight r with rightwards arrow on top. left parenthesis straight i with hat on top space plus 5 straight j with hat on top space plus straight k with hat on top right parenthesis space equals space 5 space is

  • 10/9

  • fraction numerator 10 over denominator 3 square root of 3 end fraction
  • 3/10

  • 10/3

Solution

B.

fraction numerator 10 over denominator 3 square root of 3 end fraction

Distance between the line 
straight r with rightwards arrow on top space equals space 2 straight i with hat on top space minus 2 space straight j with hat on top space plus 3 straight k with hat on top space plus straight lambda space left parenthesis straight i with hat on top space minus straight j with hat on top space plus 4 straight k with hat on top right parenthesis space and space the space plane space straight r with rightwards arrow on top. space left parenthesis straight i with hat on top space plus 5 straight j with hat on top space plus straight k with hat on top right parenthesis space equals space 5
equation of plane is x + 5y + z = 5 ∴ Distance of line from this plane = perpendicular distance of point (2, -2, 3) from the plane
straight i. straight e space open vertical bar fraction numerator 2 minus 10 plus 3 minus 5 over denominator square root of 1 plus 5 squared plus 1 end root end fraction close vertical bar space equals space fraction numerator 10 over denominator 3 square root of 3 end fraction

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