Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x - 3y - 4z = 0.

What is the value of k?

Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x - 3y - 4z = 0.

If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct ?

Consider the following for the next three (03) items that follow

The Plane 6x + ky + 3z - 12 = 0 where k ≠ 0 meets the coordinate axes at A, B and C respectively. The equation of the sphere passing through the origin and A, B, C is x² + y² + z² - 2x - 3y - 4z = 0.

What is the equation of the line through the origin and the centre of the sphere ?

Consider the following for the next two (2) items that follow :

Let the plane $\frac{2x}{k} + \frac{2y}{3} + \frac{z}{3} = 2 $ pass through the point (2, 3, -6).

What are the direction ratios of the normal to the plane ?