The locus of intersection of locus of $P$ with $2x + y + z = 2$ is:
Step-by-Step Solution
Key Concept: A plane with restricted inclination angle through a point on the $z$-axis can degenerate into a pair of straight lines.
The plane passes through $(0,0,2)$ with inclination angle $\theta$ to the $z$-axis where $\sin\theta = \frac{1}{\sqrt{6}}$. For $0 < \theta < 60°$, the plane's intersection with 3D space simplifies to a pair of straight lines in the $xy$-plane, since the constraint on the inclination limits the plane's tilt sufficiently.
Correct Answer: 1