Lines and Triangles

Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its third side passes through the point $$(1, -10)$$. Determine the equation of the third side.
Find foot of the $$\perp$$ from the point (2, 3) on the line $$3x-y+4=0$$
Let $$A(3,\ 2,\ 0),\ B(5,\ 3,\ 2),\ C(-9,\ 6,\ -3)$$ be three points forming a triangle. $$AD$$, the bisectors of $$\angle BAC$$,meets $$BC$$ an $$D$$. Find the coordinates of the point $$D$$. 
$$PQRS$$ is a square, $$T$$ and $$U$$ are the mid-points of the sides $$PS$$ and $$QR$$ respectively. find the area of  $$\Delta OTS$$, if $$PS=8cm$$,where O is the point of intersection of $$TU$$ and $$OS$$.
In a $$\triangle ABC$$ right angled at C, if $$\tan { A=\frac { 1 }{ \sqrt { 3 }  }  } $$ find the value of $$\sin { A } \cos { B } +\cos { A } \sin { B } $$