Determining the Uncertainty of a Unit Vector using Error Propagation

[thefelonwind]

Homework Statement

Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values given.

Homework Equations

unit vector = u/||u||

The Attempt at a Solution

My result for the unit vector is:
unit vector=(10/sqrt(110)*i + (1/sqrt(110))*j
(where i and j represent i-hat and j-hat, the vector components)

I believe this is correct because when I calculate the magnitude of the unit vector using those components, I get 1 as my answer.

Where I am stuck at is calculating the uncertainty in u using error propagation. Can anybody get me on the right track for figuring that out? I've not used error propagation yet (this is for a Introductory Physics Lab) and do not have a single clue where to start.

 

[Redbelly98]

Welcome to Physics Forums.

The Attempt at a Solution

My result for the unit vector is:
unit vector=(10/sqrt(110)*i + (1/sqrt(110))*j
(where i and j represent i-hat and j-hat, the vector components)

I believe this is correct because when I calculate the magnitude of the unit vector using those components, I get 1 as my answer.

Yes, that looks good. Also note the i and j parts are in the ratio of 10:1, just as the displacement vector is.

Where I am stuck at is calculating the uncertainty in u using error propagation. Can anybody get me on the right track for figuring that out? I've not used error propagation yet (this is for a Introductory Physics Lab) and do not have a single clue where to start.

I've not seen a problem quite like this one before, but they must mean that there is an error in the angle of the unit vector (the magnitude is exactly 1 by definition).

Can you adjust each given coordinate by ±2, in order to get the direction of the vector to change by the largest possible angle? The resulting unit vector vector you get that way should give an indication of the error.