(i) To find the components of the 8 N force:

1. Parallel to the 10 N force: The component is \(8 \cos \theta\). Therefore, the resultant component parallel to the 10 N force is \(10 - 8 \cos \theta\).
2. Perpendicular to the 10 N force: The component is \(8 \sin \theta\).

(ii) The magnitude of the resultant force is given as 8 N. Using the Pythagorean theorem for the components:

\((10 - 8 \cos \theta)^2 + (8 \sin \theta)^2 = 8^2\)

Expanding and simplifying:

\(100 - 160 \cos \theta + 64 \cos^2 \theta + 64 \sin^2 \theta = 64\)

Using \(\sin^2 \theta + \cos^2 \theta = 1\):

\(100 - 160 \cos \theta + 64 = 64\)

\(164 - 160 \cos \theta = 64\)

\(160 \cos \theta = 100\)

\(\cos \theta = \frac{5}{8}\)