3d geometry Questions

The intersection of the spheres $x^2+y^2+z^2+7x-2y-z=13$ and $x^2+y^2+z^2-3x+3y+4z=8$ is the same as the intersection of one of the sphere and the plane

Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is

A line with direction cosines proportional to $2,1,2$ meets each of the lines $x=y+a=z$ and $x+a=2y=2z.$ The co-ordinates of each of the point of intersection are given by

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

If the straight lines $x=1+s,y=-3-\lambda s,z=1+\lambda s$ and $x=\frac{t}{2},y=1+t,z=2-t$ with parameters $s$ and $t$ respectively, are co-planar then $\lambda$ equals