Search any question & find its solution
Question:
Answered & Verified by Expert
A line makes angles $\theta, \phi$ and $\psi$ with $\mathrm{x}, \mathrm{y}, \mathrm{z}$ axes respectively.
Consider the following
1 . $\sin ^{2} \theta+\sin ^{2} \phi=\cos ^{2} \psi$
2 . $\quad \cos ^{2} \theta+\cos ^{2} \phi=\sin ^{2} \psi$
3 . $\sin ^{2} \theta+\cos ^{2} \phi=\cos ^{2} \psi$
Which of the above is/are correct?
Options:
Consider the following
1 . $\sin ^{2} \theta+\sin ^{2} \phi=\cos ^{2} \psi$
2 . $\quad \cos ^{2} \theta+\cos ^{2} \phi=\sin ^{2} \psi$
3 . $\sin ^{2} \theta+\cos ^{2} \phi=\cos ^{2} \psi$
Which of the above is/are correct?
Solution:
2154 Upvotes
Verified Answer
The correct answer is:
2 only
If a line makes angle $\theta, \phi$ and $\psi$ with $\mathrm{x}, \mathrm{y}, \mathrm{z}$ axes respectively, then $\cos ^{2} \theta+\cos ^{2} \phi+\cos ^{2} \psi=1$
$\Rightarrow \cos ^{2} \theta+\cos ^{2} \phi=1-\cos ^{2} \psi \Rightarrow \cos ^{2} \theta+\cos ^{2} \phi=\sin ^{2} \psi$
Statement $(2)$ is correct
$\Rightarrow \cos ^{2} \theta+\cos ^{2} \phi=1-\cos ^{2} \psi \Rightarrow \cos ^{2} \theta+\cos ^{2} \phi=\sin ^{2} \psi$
Statement $(2)$ is correct
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.