Finding components of a force vector given length components of vector

[adam199]

Homework Statement

A horseback rider is pulling a log behind him attached via a rope. The force of tension along the rope is 2000 N. What are the vector components of this force given the length components of the rope? The length components are x=1.5m y=2m z=2m. This problem is 3D so there are x,y,z components.

Homework Equations

x^2+y^2+z^2 equals the length of the rope

The Attempt at a Solution

My guess at the solution to this problem is to find the length of the rope using the lengths of the component vectors, and then using the ratios between these components and the length vector to find the force components.

 

[frogjg2003]

The tension of the rope is in a direction along the line of the rope, so yes, you're right.