Force vector in a new coordinate frame?

[theBEAST]

Homework Statement

http://img811.imageshack.us/img811/9092/captureykj.png

The Attempt at a Solution

The answer is also in the image above. I have no clue how to start this question. Could anyone be so kind to give me a hint on how I should approach this question? Thanks!

 

[gabbagabbahey]

Homework Statement

http://img811.imageshack.us/img811/9092/captureykj.png

The Attempt at a Solution

The answer is also in the image above. I have no clue how to start this question. Could anyone be so kind to give me a hint on how I should approach this question? Thanks!

The statement "\mathbf{f} is measured as \begin{bmatrix} 1 \\ -1\end{bmatrix}\text{N} in the u, v coordinate basis" means that \mathbf{f} = (1 \text{N})\mathbf{e}_u +(-1\text{N}) \mathbf{e}_v. So, if you can do a little trig to express \mathbf{e}_u & \mathbf{e}_v in terms of \mathbf{e}_x & \mathbf{e}_y, you can express \mathbf{f} in the x, y coordinate basis.

Hint: \mathbf{A} \cdot \mathbf{B} = ||\mathbf{A}||||\mathbf{B}|| \cos \theta, where \theta is the angle between the two vectors.