If a line makes an angle of π/4 with the positive directions of each of x -axis and y -axis, then the angle that the line makes with the positive dire - Mathematics MCQ AIEEE 2007 2026 | ExamTest.live

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If a line makes an angle of π /4 with the positive directions of each of x -axis and y -axis, then the angle that the line makes with the positive direction of the z -axis is:

Solution & Step-by-step Explanation

Let the angles be α, β, γ . Given α = π /4 and β = π /4 .The direction cosines l, m, n are l = cos α, m = cos β, n = cos γ .We know that l^{2} + m^{2} + n^{2} = 1 . cos^{2} (π /4) + cos^{2} (π /4) + cos^{2} γ = 1 (\frac{1}{2})^{2} + (\frac{1}{2})^{2} + cos^{2} γ = 1 \frac{1}{2} + \frac{1}{2} + cos^{2} γ = 1 1 + cos^{2} γ = 1 ⟹ cos^{2} γ = 0 cos γ = 0 ⟹ γ = π /2 The line makes an angle of π /2 with the z -axis.

Try it yourself before checking the explanation above.

If a line makes an angle of π /4 with the positive directions of each of x -axis and y -axis, then the angle that the line makes with the positive direction of the z -axis is:

π /6

π /3

π /4

π /2

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