Final answer:
To find the magnitude and direction of the resultant force Fr (F1 + F2), we add the components of F1 and F2 to determine Fr. The magnitude is calculated using the Pythagorean theorem, based on the vector components. The force's direction is determined using inverse trigonometric functions for the angles.
Step-by-step explanation:
To determine the magnitude of the resultant force Fr = F1 + F2 and its direction measured counterclockwise, we can use vector addition. Since force is a vector quantity, we can break down the forces into their components and then sum up the corresponding components to get the resultant force.
Given the components of F1 are 10.0 N along the x-axis, -20.4 N along the y-axis, and 2.0 N along the z-axis, and the components of F2 are -15.0 N along the x-axis, 0.0 N along the y-axis, and -6.2 N along the z-axis, we can find the resultant force vector Fr by adding the components of F1 and F2:
- Frx = F1x + F2x = 10.0 N - 15.0 N = -5.0 N
- Fry = F1y + F2y = -20.4 N + 0.0 N = -20.4 N
- Frz = F1z + F2z = 2.0 N - 6.2 N = -4.2 N
The magnitude of Fr is then calculated using the Pythagorean theorem for three-dimensional vectors: Fr = √((-5.0 N)² + (-20.4 N)² + (-4.2 N)²).
The direction of Fr is found by calculating the angle θ concerning the positive direction of the axes with the use of inverse trigonometric functions like arctan.