$ABC$ is a triangle right-angled at B. If A(k,1,−1), B(2k,0,2) and $C(2+2k,k,1)$ are the vertices of the triangle, then what is the value of k?

If a line  $\frac{x+1}{p} = \frac{y-1}{q} = \frac{z-2}{r}$  where $p=2q=3r$, makes an angle θ with the positive direction of y-axis, then what is cos2θ equal to?

What is the equation of the plane passing through the point (1,1,1) and perpendicular to the line whose direction ratios are (3,2,1)?

Direction: Consider the following for the items that follow:

Let 2x² + 2y² + 2z² + 3x + 3y + 3z - 6 = 0 be a sphere.

What is the diameter of the sphere?