Adding/Subtracting Vectors - Resultant Magnitude Change?

[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?

 

[wais]

Yes, you are correct. The magnitude of the resultant vector can change when subtracting vectors. This is because the direction of the resultant vector is determined by the angle between the two vectors being added or subtracted. In your example, if vector b is subtracted from vector a, the resultant vector will have a larger magnitude because the angle between them will be obtuse (greater than 90 degrees). This means that the two vectors are pointing in opposite directions, resulting in a larger overall magnitude. However, if the angle between the two vectors is acute (less than 90 degrees), the resultant vector will have a smaller magnitude when vector b is subtracted from vector a. So, the magnitude of the resultant vector can change depending on the angles and directions of the vectors being added or subtracted.