WBJEE · Maths · Three Dimensional Geometry
The plane \(\ell \mathrm{x}+\mathrm{my}=0\) is rotated about its line of intersection with the plane \(\mathrm{z}=0\) through an angle \(\alpha\). The equation changes to
- A \(\ell \mathrm{x}+\mathrm{my} \pm \tan \alpha \sqrt{\ell^{2}+\mathrm{m}^{2}}=0\)
- B \(\ell \mathrm{x}+\mathrm{my} \pm \mathrm{z} \tan \alpha \sqrt{\ell^{2}+\mathrm{m}^{2}+1}=0\)
- C \(\ell \mathrm{x}+\mathrm{my} \pm \mathrm{z} \tan \alpha \sqrt{\ell^{2}+1}=0\)
- D \(\ell \mathrm{x}+\mathrm{my} \pm \mathrm{z} \tan \alpha \sqrt{\ell^{2}+\mathrm{m}^{2}}=0\)
Answer & Solution
Correct Answer
(D) \(\ell \mathrm{x}+\mathrm{my} \pm \mathrm{z} \tan \alpha \sqrt{\ell^{2}+\mathrm{m}^{2}}=0\)
Step-by-step Solution
Detailed explanation
\(P_{1}: \ell x+m y=0, \quad P_{2}=z=0\) Plane through common line of \(P_{1}\) and \(P_{2}\) \(\mathrm{P}_{3}: \ell \mathrm{x}+\mathrm{my}+\mathrm{nz}=0\) angle between \(P_{1}\) and \(P_{3}=\alpha\) \(\therefore \cos \alpha=\hat{n}_{1}, \hat{n}_{2}\)…
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