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
- A \(\pm \sqrt{2}\)
- B \(\pm \sqrt{3}\)
- C \(\pm 2\)
- D \(\pm 3\)
Answer & Solution
Correct Answer
(B) \(\pm \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Direction cosine of line is \(\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)\). \(\therefore \quad \frac{1}{c^2}+\frac{1}{c^2}+\frac{1}{c^2}=1\) \(\Rightarrow \quad \frac{3}{c^2}=1 \Rightarrow c^2=3\) \(\therefore \quad c= \pm \sqrt{3}\)
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