Question

The plane $lx+my=0$ is rotated about its line of intersection with the plane z = 0 through an angle $\theta$. Then the equation to the plane in new position is

• A. $lx+my\pm z\sqrt{l^2+m^2}tan\theta =0$
• B. $lx+my\pm z\sqrt{l^2-m^2}cot\theta =0$
• C. $lx+my\pm z\sqrt{l^2+m^2}cot\theta =0$
• D. $lx+my\pm z\sqrt{l^2-m^2}tan\theta =0$

Answer 1

The correct option is A $lx+my\pm z\sqrt{l^2+m^2}tan\theta =0$

Equation of the required plane is

$lx+my+\lambda z=\mathrm{0........}\left(i\right)$

angle between (i) and $lx+my=0$ is $\alpha$

$⟹co{s}^2\alpha =\frac{l^2+m^2}{l^2+m^2+{\lambda }^2}=\lambda =\pm \sqrt{l^2+m^2}$

Hence equation of plane is

$lx+my\pm z\sqrt{l^2+m^2}tan\theta =0$