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JEE Main2012MathematicsThree Dimensional GeometryActual

The coordinates of the foot perpendicular from the point (1,0,0) to the line x-1 2 = y+1 -3 = z+10 8 are

Options

  1. A(2,-3,8)
  2. B(1,-1,-10)
  3. C(5,-8,-4)
  4. D(3,-4,-2)

Correct answer

D. (3,-4,-2)

Step-by-step solution

Let the equation of A B is x-1 2 = y-(-1) -3 = z-(-10) 8 =k Let L be the foot of the perpendicular drawn form P(1,0,0) . L=(2 k+1,-3 k -1,8 k-10) . Now, direction ratio of P L=(2 k,-3 k-1,8-10) and direction ratio of A B=(2,-3,8) Since, P L is perpendicular to A B 2(2 k)-3(-3 k-1)+8(8 k-10)=0 Now, k= 2(1-1)+(-3)(0+1)+8(0+10) (2)^2+(-3)^2+(8)^2 = 0-3+80 4+9+64 = 77 77 =1 Required co-ordinate =L=(2+1,-3-1,8-10)=(3,-4,-2) .

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