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AP EAMCET · Maths · Three Dimensional Geometry

If the direction cosines of a straight line are \(\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)\), then \(c\) is equal to

  1. A \(\pm \sqrt{2}\)
  2. B \(\pm \sqrt{3}\)
  3. C \(\pm 2\)
  4. D \(\pm 3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\pm \sqrt{3}\)

Step-by-step Solution

Detailed explanation

Direction cosine of line is \(\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)\). \(\therefore \quad \frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1\) \(\Rightarrow \quad \frac{3}{c^2}=1 \Rightarrow c^2=3\) \(\therefore \quad c= \pm \sqrt{3}\)