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MHT CET202314 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

A line with positive direction cosines passes through the point P (2,-1,2) and makes equal angles with the co-ordinate axes. The line meets the plane 2 x+y+z=9 at point Q . The length of the line segment P Q equals

Options

  1. A3
  2. B2
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

Since direction cosines of PQ are equal and positive. The d.r.s. of PQ are 1 3 , 1 3 , 1 3 The equation of the line PQ is aligned & x-2 1 3 = y+1 1 3 = z -2 1 3 & x-2=y+1= z -2= k , say aligned Co-ordinates of the point Q are ( k +2, k -1, k +2) The point Q lies on the plane 2 x+y+z=9 array ll & 2( k +2)+ k -1+ k +2=9 & 4 k +5=9 k =1 & Q (3,0,3) & PQ = (3-2)^2+(0+1)^2+(3-2)^2 & = 1+1+1 = 3 array

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