Final answer:
Work is the product of force and displacement. The work done by force F₁ can be calculated by finding the dot product of the force and displacement vectors.
Step-by-step explanation:
Work (W) is the product of the component of a force along a displacement and that displacement. To find the work done by a force, you can use the equation: W = |F| * |d| * cos(theta), where F is the force, d is the displacement, and theta is the angle between the force and displacement vectors.
In this case, the force F₁ = (3 N)i + (4 N)j and the displacement is from the origin (0 m, 0 m) to the point (5 m, 6 m). To calculate the work done by F₁, you can substitute the values into the formula and calculate the dot product:
W = (3 N * 5 m) + (4 N * 6 m) = 15 Nm + 24 Nm = 39 Nm.