To find the tensions in the strings, we resolve the forces acting on the particle P vertically and horizontally.

Vertically, the sum of the vertical components of the tensions must equal the weight of the particle:

\(T_A \frac{1}{2.6} + T_B \frac{1}{1.25} = 10.5\)

Horizontally, the horizontal components of the tensions must balance each other:

\(T_A \frac{2.4}{2.6} = T_B \frac{0.75}{1.25}\)

Solving these equations simultaneously gives:

\(T_A = 6.5 \text{ N}\)

\(T_B = 10 \text{ N}\)