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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2012 · Mathematics · Three Dimensional Geometry

If a line makes the angles α, β, γ with the axes, then what is the...

If a line makes the angles α,β,γ\alpha, \beta, \gamma with the axes, then what is the value of 1+cos⁡2α+cos⁡2β+cos⁡2γ1+\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma equal to?

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

B. 0

Step-by-step solution

cos⁡2α+cos⁡2β+cos⁡2γ=11+cos⁡2α2+1+cos⁡2β2+1+cos⁡2γ2=13+cos⁡2α+cos⁡2β+cos⁡2γ=21+cos⁡2α+cos⁡2β+cos⁡2γ=0\begin{aligned} & \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1 \\ & \frac{1+\cos 2 \alpha}{2}+\frac{1+\cos 2 \beta}{2}+\frac{1+\cos 2 \gamma}{2}=1 \\ & 3+\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma=2 \\ & 1+\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma=0\end{aligned}
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