# Undergraduate Mechanics (Problem with force expressed as basis vectors)

1. May 17, 2012

### s3a

1. The problem statement, all variables and given/known data
The problem along with its solution is attached as Problem 1-2.jpg.

2. Relevant equations
Norm of a vector.

3. The attempt at a solution
Starting from the final answer of the solution, sqrt((-0.625)^2 + (0.333)^2) == 0.708176532 != 1. Did the book do something wrong? I ask because, a unit vector should have a magnitude of 1. Also, sin(ϕ) = sin(60°) should equal 0.866025404 rather than 0.883 and cos(ϕ) = cos(60°) should equal 0.5 instead of 0.470. Am I missing something here?

Any input would be greatly appreciated!

#### Attached Files:

• ###### Problem 1-2.jpg
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2. May 17, 2012

### Staff: Mentor

It looks like they're not requiring the basis vectors to be unit vectors (although they've specified e1 to be of unit length). Also, the angle $\phi$ is actually not precisely 60°, which you can work out from the calculated side lengths of the small triangle.

3. May 18, 2012

### s3a

Thanks for pointing those out; I've now confirmed the numbers are correct in the solutions. Just to make sure I understood you correctly, it is wrong that they put a caret (^) on top of the e_2 basis vector, right? Other than that everything is correct, right?

4. May 18, 2012

### Staff: Mentor

In general the caret on a variable can simply be taken to mean that it is a vector. Some publications use it to imply that the vector is a unit vector of a basis set in order to distinguish them from other vector variables. It is not a mandatory restriction, and in fact there's no mathematical necessity for basis vectors to be measured in units that make them have length "1", even if it is a practical convenience. So while it may not be conventional or esthetically pleasing to have the caret on the e2 basis vector when it's not of unit length, it's not technically incorrect.

5. May 23, 2012

### s3a

Thanks again :).