ExamBro
ExamBro
AP EAMCET · Maths · Three Dimensional Geometry

If the sum of the distances of the point \((3,4, \alpha), \alpha \in \mathrm{R}\) from X -axis, Y -axis and Z-axis is minimum, then \(\sec \alpha=\)

  1. A \(2\)
  2. B \(1\)
  3. C \(0\)
  4. D \(-1\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1\)

Step-by-step Solution

Detailed explanation

\( \text{Let } D(\alpha) = \sqrt{4^2 + \alpha^2} + \sqrt{3^2 + \alpha^2} + \sqrt{3^2 + 4^2} \) \( D(\alpha) = \sqrt{16 + \alpha^2} + \sqrt{9 + \alpha^2} + 5 \) \( \frac{dD}{d\alpha} = \frac{2\alpha}{2\sqrt{16 + \alpha^2}} + \frac{2\alpha}{2\sqrt{9 + \alpha^2}} = 0 \)…