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Question
If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
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Solution
We have
α=90°
β=60°
γ=θ
Since cos2α+cos2β+cos2γ=1,
`cos^2(90°)+cos^2(60°)+cos^2θ=1 `
`0^2+(1/2)^2+cos^2θ=1`
`cos^2θ=1−1/4=3/4`
`cosθ=sqrt3/2 (θ is acute.)`
`∴ θ=30°`
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