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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Three Dimensional Geometry

NDA 2013 · Mathematics · Three Dimensional Geometry

If a line makes 30^ ^ with the positive direction of x -axis, angle...

If a line makes 30∘30^{{}^{\circ}} with the positive direction of xx-axis, angle β\beta with the positive direction of yy-axis and angle γ\gamma with the positive direction of zz-axis, then what is cos⁡2β+cos⁡2γ\cos ^2 \beta+\cos ^2 \gamma equal to?

Options

  1. A1/41 / 4
  2. B1/21 / 2
  3. C3/43 / 4
  4. D11

Correct answer

A. 1/41 / 4

Step-by-step solution

cos⁡230∘+cos⁡2β+cos⁡2γ=1⇒cos⁡2β+cos⁡2γ=14\begin{aligned} & \cos ^2 30^{{}^{\circ}}+\cos ^2 \beta+\cos ^2 \gamma=1 \\ & \Rightarrow \quad \cos ^2 \beta+\cos ^2 \gamma=\frac{1}{4}\end{aligned}
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