In the context of vectors and scalars, what is meant by the magnitude of a force vector?

• A. The rate at which the force changes with time, measured in newtons per second (N/s)
• B. The net displacement produced by the force over time, measured in meters (m)
• C. The direction in which the force acts, measured as an angle from a reference axis
• D. The numerical size (strength) of the force, independent of its direction, measured in newtons (N)

Answer: (D)

Verified step by step guidance

1. Understand that a force is a vector quantity, which means it has both magnitude and direction.
2. The magnitude of a force vector refers to its numerical size or strength, without considering the direction in which it acts.
3. Magnitude is a scalar quantity, so it is always a non-negative value and is measured in newtons (N) in the SI system.
4. To find the magnitude of a force vector \( \vec{F} = (F_x, F_y, F_z) \), use the formula for the length of a vector: \[ \\text{Magnitude} = |\vec{F}| = \sqrt{F_x^2 + F_y^2 + F_z^2} \]
5. Remember that the magnitude tells you how strong the force is, but it does not provide any information about the direction in which the force acts.