AP EAMCET · Maths · Three Dimensional Geometry
If a line L makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{4}\) with Y -axis and Z -axis respectively, then the angle between L and another line having direction ratios \(1,1,1\) is
- A \(\cos ^{-1}\left(\frac{2}{\sqrt{6}}\right)\)
- B \(\cos ^{-1}\left(\frac{\sqrt{2}+1}{3 \sqrt{3}}\right)\)
- C \(\cos ^{-1}\left(\frac{\sqrt{2}-1}{3}\right)\)
- D \(\cos ^{-1}\left(\frac{\sqrt{2}+1}{\sqrt{6}}\right)\)
Answer & Solution
Correct Answer
(D) \(\cos ^{-1}\left(\frac{\sqrt{2}+1}{\sqrt{6}}\right)\)
Step-by-step Solution
Detailed explanation
L makes \(\frac{\pi}{3}\) and \(\frac{\pi}{4}\) angle with Y -axis and Z -axis \(\therefore m=\cos \frac{\pi}{3}=\frac{1}{2}\) and \(n=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}\) and \(l^2+m^2+n^2=1 \Rightarrow l^2+\frac{1}{4}+\frac{1}{2}=1 \Rightarrow l=\frac{1}{2}\) Now, angle…
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