A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?

Consider the following statements :

1. The direction ratios of y-axis can be <0, 4, 0>

2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0>

Which of the statements given above is/are 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 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 ?