AP EAMCET · Maths · Three Dimensional Geometry
A straight line is equally inclined to all the three coordinate axes. Then, an angle made by the line with the \(y\)-axis is
- A \(\cos ^{-1}\left(\frac{1}{3}\right)\)
- B \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
- C \(\cos ^{-1}\left(\frac{2}{\sqrt{3}}\right)\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)\)
Step-by-step Solution
Detailed explanation
Since, a line is equally inclined to the coordinate axes. \(\begin{array}{ll}\therefore & l-m=n \\ \because & l^2+m^2+n^2=1 \\ \Rightarrow & 3 l^2=1 \\ \Rightarrow & l= \pm \frac{1}{\sqrt{3}}\end{array}\) \(\therefore\) Angle made by line with \(y\)-axis…
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