Question

If $l,m$ are the direction cosines of a line lying in the $xy$ plane, then

• A. $l^2+m^2=0$
• B. $l^2+m^2=1$
• C. $l^2+m^2=C$
• D. None of these

Answer 1

Answer: (B)

$l^2+m^2=1$

we know that

if the line makes $\alpha$ angle with $x-axis$ and $\beta$ angle with $y-axis$

$\cos \alpha =l$

$\cos \beta =m$

${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma =1$

${\cos }^2\alpha +{\cos }^2\beta +0=1$

${\cos }^2\alpha +{\cos }^2\beta =1$

$l^2+m^2=1$