(i) To find P, use the formula for the magnitude of a vector:

\(P = \sqrt{(-2.8)^2 + 9.6^2} = \sqrt{7.84 + 92.16} = \sqrt{100} = 10 \text{ N}\).

To find R, use the Pythagorean theorem for the resultant of perpendicular forces:

\(R = \sqrt{10^2 + 25^2} = \sqrt{100 + 625} = \sqrt{725} \approx 26.9 \text{ N}\).

(ii) To find α, use the tangent function:

\(\tan \alpha = \frac{9.6}{2.8}\), so \(\alpha = \arctan\left(\frac{9.6}{2.8}\right) \approx 73.7^\circ\).

For the components of the 25N force:

(a) x-direction: \(25 \cos(90^\circ - \alpha) = 25 \sin(\alpha) \approx 24 \text{ N}\).

(b) y-direction: \(25 \sin(90^\circ - \alpha) = 25 \cos(\alpha) \approx 7 \text{ N}\).

(iii) To find θ, use the tangent function for the resultant vector:

\(\tan \theta = \frac{7 + 9.6}{24 - 2.8}\), so \(\theta = \arctan\left(\frac{16.6}{21.2}\right) \approx 38.1^\circ\).