Search any question & find its solution
Question:
Answered & Verified by Expert
If the direction cosines of two lines are such that $l+m+n=0, l^2+m^2-n^2=0$, then the angle between them is :
Options:
Solution:
2163 Upvotes
Verified Answer
The correct answer is:
$\pi / 3$
If $l, m, n$ are direction cosines of two lines are such that
$l+m+n=0$ $\ldots$ (i)
$l^2+m^2-n^2=0$ ...(ii)
and $l^2+m^2+n^2=1$ ...(iii)
On solving Eqs. (i), (ii) and (iii), we get $l=0, m= \pm \frac{1}{\sqrt{2}}$ and $n= \pm \frac{1}{\sqrt{2}}$
$\therefore$ Angle between these two lines
$=\frac{\pi}{3} \text { or } \frac{\pi}{2}$
$l+m+n=0$ $\ldots$ (i)
$l^2+m^2-n^2=0$ ...(ii)
and $l^2+m^2+n^2=1$ ...(iii)
On solving Eqs. (i), (ii) and (iii), we get $l=0, m= \pm \frac{1}{\sqrt{2}}$ and $n= \pm \frac{1}{\sqrt{2}}$
$\therefore$ Angle between these two lines
$=\frac{\pi}{3} \text { or } \frac{\pi}{2}$
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.