If the tangent at a point P on the parabola $\mathrm { y } ^ { 2 } = 3 \mathrm { x }$ is parallel to the line $x + 2 y = 1$ and the tangents at the points $Q$ and $R$ on the ellipse $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 1 } = 1$ are perpendicular to the line $x - y = 2$, then the area of the triangle $P Q R$ is:
(1) $\frac { 9 } { \sqrt { 5 } }$
(2) $5 \sqrt { 3 }$
(3) $\frac { 3 } { 2 } \sqrt { 5 }$
(4) $3 \sqrt { 5 }$