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Question

The foot of the perpendicular from P(1, 0, 2) to the line
x+13=y+12=z+11​  is the point
  1. (2, 3, 6)
  2. (1,2,3)
  3. (2, 4, –6)
  4. (12,1,32)


Solution

The correct option is D (12,1,32)
x+13=y+12=z+11=r

M(3r1,2r+2,r1)
DR’s of PM are 3r – 2, –2r + 2, –r – 1
DR’s of line QM are 3, –2, –1
  9r – 6 + 4r – 4 + r + 3 = 0
14r7=0r=12M(12,1,32)

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