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The direction cosines of any normal to the XY plane are
  • a)
    < 1 , 1 , 0 >
  • b)
    < 0 , 0 , 1 >
  • c)
    < 1 , 0 , 0 >
  • d)
    < 0 , 1 , 0 >
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The direction cosines of any normal to the XY plane area)<1 , 1 , 0...
Any normal of x−y plane is along z−axis.
normal unit vector to x−y plane, 
n→ = kˆ= 0iˆ+0jˆ+1kˆ
Direction cosines are <0, 0, 1> or
n→ = k =0iˆ+0jˆ−1kˆ
Direction cosines are <0, 0, −1>
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Most Upvoted Answer
The direction cosines of any normal to the XY plane area)<1 , 1 , 0...
The XY plane is a plane parallel to the X and Y axes and passing through the origin. Any normal to the XY plane will be perpendicular to the plane and will have its direction vector pointing in the direction of the Z-axis.

The direction cosines of a vector are the cosines of the angles it makes with the positive X, Y, and Z axes. Since the direction of the normal vector is along the Z-axis, its direction cosines will be (0,0,1).
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The direction cosines of any normal to the XY plane area)<1 , 1 , 0...
B
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