A rectangular loop of area 2.5 m^2 lies flat in the x-z plane. A...

Since the rectangular loop lies in the x-z plane, its area vector is directed along the y-axis (perpendicular to the plane).

Thus, the area vector can be written as $\vec{A} = 2.5 \hat{j} \text{ m}^2$.

The magnetic flux $\Phi$ is the dot product of the magnetic field vector and the area vector:

$\Phi = \vec{B} \cdot \vec{A}$

$\Phi = (0.3 \hat{i} - 0.4 \hat{j} + 1.2 \hat{k}) \cdot (2.5 \hat{j})$

$\Phi = (-0.4) \times 2.5 = -1.0 \text{ Wb}$

The magnitude of the magnetic flux is $1.0 \text{ Wb}$.

Answer: $1.0 \text{ Wb}$