A plane P passes through the line of intersection of the planes 2x $$-$$ y + 3z = 2, x + y $$-$$ z = 1 and the point (1, 0, 1).

What is the equation of the plane P?

If the plane P touches the sphere $${x^2} + {y^2} + {z^2} = {r^2}$$, then what is r equal to?

The length of the normal from origin to the plane x + 2y $$-$$ 2z = 9 is equal to

If $$\alpha$$, $$\beta$$ and $$\gamma$$ are the angles which the vector OP (O being the origin) makes with positive direction of the coordinate axes, then which of the following are correct?

1. $${\cos ^2}\alpha + {\cos ^2}\beta = {\sin ^2}\gamma $$

2. $${\sin ^2}\alpha + {\sin ^2}\beta = {\cos ^2}\gamma $$

3. $${\sin ^2}\alpha + {\sin ^2}\beta + {\sin ^2}\gamma = 2$$

Select the correct answer using the code given below.