All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\left( { - 1,\,2} \right)$$ satisfy

A vector $$\overline a $$ has components $$2p$$ and $$1$$ with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system, $$\overline a $$ has components $$p + 1$$ and $$1$$, then

Let $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1}$$ $$ \ne $$ $${z_2}$$ and $$\left| {{z_1}} \right| =\,\left| {{z_2}} \right|$$. If $${z_1}$$ has positive real and $${z_2}$$ has negative imaginary part, then $${{{z_1}\, + \,{z_2}} \over {{z_1}\, - \,{z_2}}}$$ may be

The equation of the line passing through the points of intersection of the circles $$3{x^2} + 3{y^2} - 2x + 12y - 9 = 0$$ and $${x^2} + {y^2} - 6x + 2y - 15 = 0$$ is..............................