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NDA2015MathematicsThree Dimensional GeometryActual

From the point P(3,-1,11) , a perpendicular is drawn on the line L given by the equation x 2 = y-2 3 = z-3 4 . Let Q be the foot of the perpendicular. What is the length of the line segment PQ?

Options

  1. A47 units
  2. B7 units
  3. C53 units
  4. D8 units

Correct answer

C. 53 units

Step-by-step solution

Now x ₂- x ₁=-1 array ll & x ₂-3=-1 & x ₂=2 array Similarly, array ll & y ₂- y ₁=6 & y ₂+1=6 & y ₂=5 and & z ₂- z ₁=-4 & z ₂-11=-4 & z ₂=-4+11=7 array Co-ordinate of Q is (2,5,7) Length of segment PQ aligned & = (2-3)^2+(5+1)^2+(7-11)^2 & = 1+36+16 = 53 units. aligned Option (C) is correct.

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