If $$z=x+iy$$ satisfies the condition $$|z+1|=1$$, then $$z$$ lies on the

If $$3 \hat{j}, 4 \hat{k}$$ and $$3 \hat{j}+4 \hat{k}$$ are the position vectors of the vertices $$A, B, C$$ respectively of $$\triangle A B C$$, then the position vector of the point in which the bisector of $$\angle \mathrm{A}$$ meets $$\mathrm{BC}$$ is

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

In a triangle $$\mathrm{ABC}$$, with usual notations $$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5$$, then $$\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{\cos \mathrm{C}}{\mathrm{c}}=$$