Question

The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α, then the equation of the plane is lx + my + nz = 0 where n is

(a) \(\pm \sqrt{(l^2 + m^2)} cos\alpha\)

(b) \(\pm \sqrt{(l^2 - m^2)} sin\alpha\)

(c) \(\pm \sqrt{(l^2 + m^2)} tan\alpha\)

(d) \(\pm \sqrt{(l^2 - m^2)} sec\alpha\)

Answer 1

Correct option is (c) \(\pm \sqrt{(l^2 + m^2)} tan\alpha\) 

Given planes are lx + my = 0 .........(1) & z = 0............(2) 

\(\therefore\) Equation of the plane passing through the line of intersection of planes (1) & (2) is 

lx + my +λz = 0 ............(3)

D.r's of normal to (3) are l, m, λ

D.r's of normal to (1) are l, m, 0