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A vector n is inclined to x -axis at 45^ , to y -axis at 60^ and at an acute angle to z -axis. If n is a normal to a plane passing through the point ( 2 ,-1,1) then the equation of the plane is :

Options

  1. A4 2 x+7 y+z-2
  2. B2 x+y+2 z=2 2 +1
  3. C3 2 x-4 y-3 z=7
  4. D2 x-y-z=2

Correct answer

B. 2 x+y+2 z=2 2 +1

Step-by-step solution

Direction cosines of n are 1 2 , 1 4 , 1 2 . Equation of the plane, aligned & 1 2 (x- 2 )+ 1 4 (y+1)+ 1 2 (z-1)=0 & 2(x- 2 )+(y+1)+2(z-1)=0 & 2 x+y+2 z=2 2 -1+2 & 2 x+y+2 z=2 2 +1 aligned

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