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AP EAMCET · Maths · Three Dimensional Geometry

If \(-2, \frac{4}{3}, \frac{-4}{5}\) are the intercepts made by a plane on \(\mathrm{X}, \mathrm{Y}, \mathrm{Z}\)-axes respectively then the direction cosines of a normal to this plane are

  1. A \(\left(\frac{-1}{3}, \frac{2}{3}, \frac{-2}{3}\right)\)
  2. B \(\left(\frac{2}{3 \sqrt{5}}, \frac{-4}{3 \sqrt{5}}, \frac{5}{3 \sqrt{5}}\right)\)
  3. C \(\left(\frac{-4}{\sqrt{57}}, \frac{4}{\sqrt{57}}, \frac{-5}{\sqrt{57}}\right)\)
  4. D \(\left(\frac{2}{\sqrt{38}}, \frac{-3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\left(\frac{2}{\sqrt{38}}, \frac{-3}{\sqrt{38}}, \frac{5}{\sqrt{38}}\right)\)

Step-by-step Solution

Detailed explanation

If plane makes intercepts \(a, b, c\) then equation of plane is \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\) for \(-2,4 / 3,-4 / 5\), equation of plane is…