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The line segment `QR` makes an angle of `60^(@)` with the positive direction of `X`-axis.
So, the bisector of the angle `PQR` will make an angle of `60^(@)` with the negative direction of `X`-axis it will therefore have angle of inclination of `120^(@)` and so, its equation is
`y-0=tan120^(@)(x-0)`
`impliesy=-sqrt(3)x`
`impliesy+sqrt(3)x=0`
Correct Answer – C
The bisector of angle PQR divides PR in the ratio PQ:QR i.e. 1:6 . So, the coordinate of the point of divison are
`((1xx3+6xx-1)/(6),(1xx3sqrt(3)+6xx0)/(1+6))=((-3)/(7),(3sqrt(3))/(7))`
Clearly , required bisector passes through Q(0,0) and `(-3//7,3sqrt(3)//7)`. So, its equation is
`y-0 =((3sqrt(3))/(7)-0)/(-(3)/(7)-0)(x-0) implies y=-sqrt(3)x implies sqrt(3)x+y=0`