The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :

The plane $$x+2y-z=4$$ cuts the sphere $${x^2} + {y^2} + {z^2} - x + z - 2 = 0$$ in a circle of radius

A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.

If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta $$ equals :

Distance between two parallel planes

$$\,2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is :