The locus of intersection of locus of $P$ with the plane $x + y + z = 1$ is:
Step-by-Step Solution
Key Concept: When a plane does not pass through a fixed point and makes an acute angle less than $60°$ with the $z$-axis, the cross-section forms a hyperboloid.
The plane does not pass through $(0,0,2)$ and has inclination $\theta$ with the $z$-axis where $\sin\theta=\frac{1}{\sqrt{3}}$. Since $\sin\theta=\frac{1}{\sqrt{3}} < \sin 60°=\frac{\sqrt{3}}{2}$, we have $\theta < 60°$. The locus with these conditions represents a hyperboloid of one sheet.
Correct Answer: 2