Vector addition

[zero1520]

Ok, my question is, if you have 2 vectors added together a+b, could the magnitude of the resultant change if u subracted a-b? say a was any magnitude at 0 degrees. and b was any magnitude say 170 degrees. if u subtracted b it would go opposite direction southeast making the resultant much larger since it makes obtuse angle right? I might be completely wrong on this.

thank you in advance.

[cepheid]

Yes, a + b will certainly not give you the same vector in magnitude or in direction as a - b (in general). The magnitude of the resultant depends crucially on the angle between the vectors; draw the vector sum triangles for several cases and you will see. Can you tell me in what case (ie for what angle theta) the resultant magnitude will be the largest? Does the result make sense physically, if you consider a vector quantity, such as force? It should.

Hint...any time you add the vectors, the resultant vector is shorter than the distance traversed in going along the "bent" path from the tail of a to the tip of b. This is analogous to the triangle inequality, right?