The easiest way to add vectors is by component. You then find the magnitude of the resultant. You cannot simply add magnitudes and get a meaningful result.
#3
SMS
9
0
??
OK, V1= of 3.0 m/s and is directed along the +x-axis. V2=2.0 m/s. So V3 = V1+V2. Right.
to add vectors you have to break them down to their x and y components. ie let's say a vector has a magnitude of 'A' and an angle of 'K', you have to get the magnitude in the x and the magnitude in the y, so Ax=A cos (K) and Ay=A sin (K), now that you broke it down to Ax and Ay you can add it to other vector that you have broken down, just add the like parts like Bx+Ax and By+Ay the use the pathagorean theom to get the resultent magnitude (x^2+y^2=z^2) where z is the resultant magnitude.
It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC).
Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?