AP EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the line making angles \(\frac{\pi}{4}, \frac{\pi}{3}\) and \(\theta\left(0 < \theta < \frac{\pi}{2}\right)\) respectively with \(\mathrm{X}, \mathrm{Y}\) and Z axes are
- A \(\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{2}\)
- B \(\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{\sqrt{3}}{2}\)
- C \(\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{\sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}}, \frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(l = \cos(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}\) \(m = \cos(\frac{\pi}{3}) = \frac{1}{2}\) \(l^2 + m^2 + n^2 = 1 \implies (\frac{1}{\sqrt{2}})^2 + (\frac{1}{2})^2 + n^2 = 1\) \(\frac{1}{2} + \frac{1}{4} + n^2 = 1 \implies \frac{3}{4} + n^2 = 1\)…
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