question_answer

Let P = (-1, 0), Q = (0, 0) and\[O_{2}^{+}\] be three points. The equation of the bisector of \[{{O}_{2}}\]is       AIEEE  Solved  Paper-2007

A) \[NO\] 

B)         \[Si,Ge,Sn\]

C)                         \[Pb\]

D)                         \[Ge{{X}_{2}}<Si{{X}_{2}}<Sn{{X}_{2}}<Pb{{X}_{2}}\]

Correct Answer: A

Solution :

Slope of QR \[=\frac{3\sqrt{3}-0}{3-0}\] \[=\sqrt{3}=\tan \theta \] Slope of the line QM \[=\tan \frac{2\pi }{3}=-\sqrt{3}\] The angle between PQR is\[\frac{2\pi }{3},\]so line OM makes an angle\[\frac{2\pi }{3}\]from positive direction of X-axis. Hence, equation of line QM is\[y=-\sqrt{3}x\] or\[\sqrt{3}x+y=0\]