If $$(2,3,5)$$ is one end of a diameter of the sphere $${x^2} + {y^2} + {z^2} - 6x - 12y - 2z + 20 = 0,$$ then the coordinates of the other end of the diameter are

Let $$L$$ be the line of intersection of the planes $$2x+3y+z=1$$ and $$x+3y+2z=2.$$ If $$L$$ makes an angle $$\alpha $$ with the positive $$x$$-axis, then cos $$\alpha $$ equals

The image of the point $$(-1, 3,4)$$ in the plane $$x-2y=0$$ is :

The two lines $$x=ay+b, z=cy+d;$$ and $$x=a'y+b' ,$$ $$z=c'y+d'$$ are perpendicular to each other if :