I'm just learning work in my physics class and, for some reason, I'm having difficulty understanding it. The problem in my homework assignment asks: A particle moves 5 m in the positive x direction while being acted upon by a constant force F = <4,2,-4>.The work done on the particle by this force is: I know that there are several useful equations which I should use when it comes to work, W = ∫F*dr K = 1/2mv^2 Ug = mgy Fs = -kx Us = 1/2kx^2 but I don't know how to apply any of these equations to this problem. I tried the first but was unsure of what F should be because F consists of i+j+k. I found the magnitude of F and plugged it into F but then didn't know what to do with the integral... so I got ride of it and just multiplied it to 5m. I got the wrong answer so I tried with another approach. Again, I got ride of the integral because it's indefinite and I wasn't sure on how to find the constant (I am taking this integral to literally? Is it more symbolic than mathematical?) but this time I decided to make F = 4 because, in the vector <x, y, z> 4 was the x, or i, component of the equation, and I got the right answer! So my question is, does this apply to all cases? If I was given dr and the vector force <x,y,z> does the work depend the direction the particle moves through? For example, F = <1,2,3>, dr = 5m. Particle moves in the x-direction, W = 5J. Particle moves in the y-direction, W = 10J. Particle moves in the z-direction, W = 15J. Thank you for taking the times to review my question.