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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

A line x-1 2 = y-2 3 = z-3 4 intersects the plane x-y+2 z+2=0 at point A . The equation of the straight line passing through A lying in the given plane and at minimum inclination with the given line is/are

Options

  1. Ax+1 1 = y+1 5 = z+1 2
  2. B5 x-y+4=0=2 y-5 z-3
  3. C5 x+y-5 z+1=0=2 y-5 z-3
  4. Dx+2 1 = y+6 5 = z+3 2

Correct answer

D. x+2 1 = y+6 5 = z+3 2

Step-by-step solution

aligned & 2 r+1-(3 r+2)+2(4 r+3)+2=0 & 7 r+7=0 & r=-1 aligned A(-1,-1,-1) required line will be projection of given line in the plane foot of of P will be on D x-1 1 = y-2 -1 = z-3 2 =- ( 1-2+2.3+2 1^2+(-1)^2+2^2 ) x-1 1 = y-2 -1 = z-3 2 = -7 6 x= -1 6 ; y= 19 6 ; z= 4 6 x+1 2 = y+1 5 = z+1 2 x+1 2 +1= y+1 5 +1= z+1 2 +1 Also, x+1 2 = y+1 5 = z+1 2 x+1 2 = y+1 5 and y+1 5 = z+1 2 aligned & 5 x-y+4=0=2 y-5 z-3 & also (5 x-y+4)+(2 y-5 z-3)=0=2 y-5 z-3 5 x+y-5 z+1=0=2 y-5 z-3 aligned

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