Three-Dimensional Force System:Problem Solving

Consider a tent tied to the ground, with the help of eye bolts, subjected to three forces.

Consider a Cartesian coordinate system, with the origin at the eye bolt. Force F₁ acts along a two-dimensional x-y plane, while force F₂ acts in a three-dimensional space. Force F₃  is along the negative x-axis.

The magnitude of the x and y components of F₁ can be obtained using a Pythagorean triplet. Using the obtained magnitudes, F₁ can be expressed in the cartesian form.

Similarly, F₂ is resolved into vertical and horizontal components. Resolving the horizontal components further, F₂ can be expressed in terms of i, j, and k unit vectors along the three axes.

Since the third force is along the negative x-axis, its y and z components are zero.

The resultant force is then obtained in its cartesian form by adding the respective components of all three forces vectorially.

The magnitude of the resultant force is calculated as the square root of the sum of the squares of all three forces acting along the respective directions.