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Integrals

Question
CBSEENMA12036112
Wired Faculty App

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ

  • 30°

  • 45°

  • 60°

  • 75°

Solution

C.

60°

cos2α +cos2β + cos2γ = 1
α = 45°,β = 120°, γ = θ
rightwards double arrow 1 half space plus space 1 fourth space equals space 1 minus cos squared space straight theta rightwards double arrow space 3 over 4 space equals space sin squared space straight theta rightwards double arrow space sin squared space straight theta space equals space open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses squared space equals space sin squared space 60 to the power of straight o straight theta space equals space 60 to the power of straight o

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