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A line makes angles θ,ϕ and ψ with x, y, z axes respectively.

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A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following $1 . sin 2 θ + sin 2 ϕ = cos 2 ψ$ 2. cos2θ+cos2ϕ=sin2ψ $3 . sin 2 θ + cos 2 ϕ = cos 2 ψ$ Which of the above is/are correct?

1 only

2 only

3 only

2 and 3

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A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following

1 . sin 2 θ + sin 2 ϕ = cos 2 ψ

2. cos2θ+cos2ϕ=sin2ψ

3 . sin 2 θ + cos 2 ϕ = cos 2 ψ

Which of the above is/are correct?

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Text solutionVerified

[b] If a line makes angle θ, ϕ and ψ with x, y, z axes respectively, then cos2θ+cos2ϕ+cos2ψ=1 ⇒cos2θ+cos2ϕ=1−cos2ψ ⇒cos2θ+cos2ϕ=sin2ψ ∴ Statement (2) is correct.

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Question Text	A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following $1 . sin 2 θ + sin 2 ϕ = cos 2 ψ$ 2. cos2θ+cos2ϕ=sin2ψ $3 . sin 2 θ + cos 2 ϕ = cos 2 ψ$ Which of the above is/are correct?
Answer Type	Text solution:1
Upvotes	150

A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following1.sin2θ+sin2ϕ=cos2ψ2. cos2θ+cos2ϕ=sin2ψ3.sin2θ+cos2ϕ=cos2ψWhich of the above is/are correct?

Text solutionVerified

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A line makes angles θ,ϕ and ψ with x, y, z axes respectively. Consider the following $1 . sin 2 θ + sin 2 ϕ = cos 2 ψ$ 2. cos2θ+cos2ϕ=sin2ψ $3 . sin 2 θ + cos 2 ϕ = cos 2 ψ$ Which of the above is/are correct?