Finding components of a force vector given length components of vector

AI Thread Summary
To find the vector components of the force exerted by the rope, first calculate the length of the rope using the formula x^2 + y^2 + z^2. Given the lengths x=1.5m, y=2m, and z=2m, the total length can be determined. The tension in the rope is 2000 N, which acts along the direction of the rope. By using the ratios of the length components to the total length, the force components can be derived. This approach effectively relates the tension force to its respective vector components in a 3D space.
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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.
 
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The tension of the rope is in a direction along the line of the rope, so yes, you're right.
 
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