Krachtvector langs een lijn

Consider a three-dimensional static example like a pole with a cable anchored to the ground. Here, a tension force is acting along the cable.

Now, consider a Cartesian coordinate system with an arbitrary origin to represent the force as a Cartesian vector.

P_A and P_B represent the position vectors for the two ends of the cable. The force vector is directed from point A to B along the same direction as the position vector P_AB. The unit vector specifies this direction.

Applying the triangle law of vector addition, the position vector along points A and B can be obtained by subtracting P_A from P_B.

Secondly, its magnitude can be found using the square root of the sum of the squares of its components.

Now, dividing the position vector by its magnitude provides the unit vector along the cable AB.

Finally, the product of the magnitude of the force vector and the unit vector expresses the force vector in the Cartesian form.