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Question 350010
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Three Dimensional Geometry: Angle between line and plane MCQ

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Angle between line and planeHardQuestion 350010

Question

A line with direction ratios (1,1,0) makes what angle with the plane x+y=0?
  1. A
    90°
    Correct
  2. B
    0°
  3. C
    45°
  4. D
    30°

Correct answer

90°

Explanation

Normal to plane x+y=0 is (1,1,0). Direction of line is (1,1,0). Since the line direction = plane normal, the line is perpendicular to the plane (angle = 90°). Check: sin θ = |a₁a₂+b₁b₂+c₁c₂|/(|d₁||n|) = |1+1+0|/(√2×√2) = 2/2 = 1 → θ = 90°.

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