Vector Components In Box Problem

Hello!
If it helps, I believe the question intends that whenever there's a vector, or demarcation of length(where it says the length of a certain segment), it means that that's a midpoint, i.e the median of that particular line.
As for the unit vectors, it's always efficient to pick your most convenient metric, around O, on the axes perpendicular to it, and mark it as [tex] \hat{x}, \hat{y}, \hat{z} [/tex]
Hope that gets your somewhere,
Daniel

 

Strictly speaking you can't find the components of these vectors because "components" have to be in a given coordinate system and there is no given coordinate system. However, I suspect they intend that you assume a coordinate system with origin at A and the three perpendicular sides of the box as axes.

So, for example, vector F3 starts at A and points in the direction of the point halfway between B and C. If you pick a coordinate system with A as origin and the three perpendicular sides of the box as x,y, and z axes, then A's coordinates are, of course, (0, 0, 0). B's coordinates are (5, 2, 3) (do you see why) and C's coordinates are (5, 2, 0). The point halfway between B and C has coordinats ((5+5)/2, (2+ 2)/2, (3+0)/2)= (5, 2, 1.5). Find the vector from (0, 0, 0) to (5, 2, 1.5), divide by its length to get a unit vector in that direction and, finally, multiply by the magnitude of F3, 25 N.