1. The problem statement, all variables and given/known data This is an example problem where you have a force F at 100N applied at an angle of 45 degrees from a horizontal u-axis. You have the u-axis at zero degrees, then 45 degrees after that you have the Force then 15 degrees after th at you have the v-axis You are asked to determine the magnitudes of the projection of the force onto the u and v axes The solution is provided, and this part of the problem I understand However, after the solution is found there is a comment that I do not understand, it says: "NOTE: These projections are not equal to the magnitudes of the components of force F along the u and v axes found from the parallelogram law I am trying to understand why this is NOT the case Perhaps I have misunderstood what the projection of a vector is, I thought that when we project a vector along two lines, we find the components of it along those two lines, so shouldn't this equal the components of the vector along those same lines found from the parallelogram law? If it's any help, here's a screenshot of the example, the part where I am confused is highlighted: https://www.dropbox.com/s/uc92zr1vyyaurmy/projectionofvector.png 2. Relevant equations A*B=ABcosθ 3. The attempt at a solution By decomposing the force of 100 N along the v and u axes respectively, using the parallelogram law I have found the force-component along the u-axis to equal 29.89N and the force-component along the v-axis to be 81.65N This proves that the projections of the vector onto the two axes u and v, do not equal the projections of the force F along these two axes which are stated in the solution for the exame to be 70.7N for the u-axis and 96.6N for the v axis So the statement at the bottom is indeed correct I assume then that I have a faulty understanding of what the projection of a vector is Paraphrasing the definition of the term "projection of a vector onto a line" the same textbook says that: The component of the a vector A parallel to a given line aa is equal to the magnitude of the vector times cosine of the angle between the vector and the line To me this seems just like finding the component of the vector along that line, so if you do it for two lines it would be just like finding the vector components along two axes, like we do when we apply parallel law theory This is where I am stuck, I know I am understand this wrong somehow, please point what it is that I am understanding wrong? Thanks!