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AP EAMCET201825 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

If a line makes angles tan - 1 7 , tan - 1 5 3 with X -axis and Y -axis respectively, then the angle made by it with Z -axis is

Options

  1. Aπ 2
  2. Bπ 6 or 5 π 6
  3. Cπ 3 or 2 π 3
  4. Dπ 4 or 3 π 4

Correct answer

D. π 4 or 3 π 4

Step-by-step solution

We know that, if a line makes an angle α ,   β   &   γ with positive direction of X - axis ,   Y - axis   &   Z - axis then cos 2 α + cos 2 β + cos 2 γ = 1     . . i Now, given angles are α = tan - 1 7 and β = tan - 1 5 3 . Then, cos tan - 1 7 = cos cos - 1 1 2 2 = 1 2 2 cos tan - 1 5 3 = cos cos - 1 3 2 2 = 3 2 2 Therefore, from i , we get ⇒ 1 2 2 2 + 3 2 2 2 + cos 2 γ = 1 ⇒ 1 8 + 3 8 + cos 2 γ = 1 ⇒

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