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MHT CET202314 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The length of the perpendicular drawn from the point (1,2,3) to the line x-6 3 = y-7 2 = z-7 -2 is

Options

  1. A4 units
  2. B5 units
  3. C6 units
  4. D7 units

Correct answer

D. 7 units

Step-by-step solution

Let x-6 3 = y-7 2 = z-7 -2 = (say) Any point on the line is P (3 +6,2 +7,-2 +7) Let A (1,2,3) The d.r.s. of line AP are aligned & 3 +6-1,2 +7-2,-2 +7-3 & i.e. 3 +5,2 +5,-2 +4 aligned Since AP is perpendicular to the given line, aligned & 3(3 +5)+2(2 +5)-2(-2 +4)=0 & 17 +17=0 & =-1 & P (3,5,9) & AP = (3-1)^2+(5-2)^2+(9-3)^2 & = 49 & =7 units aligned

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