Physics

Physics

Problem

A force F⃗=3i+4j−5k N\vec F = 3\mathbf{i} + 4\mathbf{j} - 5\mathbf{k}\,\text{N} acts on a particle that moves from the origin A(0,0,0)A(0,0,0) to the point B(6,−3,2)B(6,-3,2) (coordinates in metres). Answer the following: a. (i) Calculate the component of F⃗\vec F along the displacement AB⃗\vec{AB}. b. (ii) Find the magnitude of the component of F⃗\vec F that is perpendicular to AB⃗\vec{AB}. c. (iii) Determine the work done by the force during the displacement from AA to BB.
Intuitive explanation

This problem is about work done by a constant force, which depends only on the component of force in the direction of motion. The key insight is that work equals the dot product of force and displacement vectors—you don't need the angle between them explicitly. Set up your displacement vector from AA to BB, then multiply it component-by-component with the force vector and sum the results.

Intuitive explanation

This problem is about work done by a constant force, which depends only on the component of force in the direction of motion. The key insight is that work equals the dot product of force and displacement vectors—you don't need the angle between them explicitly. Set up your displacement vector from AA to BB, then multiply it component-by-component with the force vector and sum the results.

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