The locus of intersection of locus of $P$ and the plane $x + y + z = 2$
Step-by-Step Solution
Key Concept: When a plane passes through a fixed point and makes an acute angle with the $z$-axis where $\sin\theta=\frac{1}{\sqrt{3}}$, the intersection forms a pair of straight lines.
The plane passes through $(0,0,2)$ and has inclination $\theta$ with the $z$-axis where $\sin\theta=\frac{1}{\sqrt{3}}$. Since $\theta < 60°$ and the plane passes through the given point, the locus represents a pair of straight lines intersecting at $(0,0,2)$.
Correct Answer: 1