Answer:
a) No, Two vectors with different magnitudes can never add up to zero.
b) Yes, Three or more vectors with different magnitudes can add up to zero.
Explanation:
a) No, Two vectors with different magnitudes can never add up to zero.
Given vector A and B
A = (x1,y1,z1) and B = (x2,y2,z2)
For A + B = 0
This conditions must be satisfied.
x1 + x2 = 0
y1 + y2 = 0
z1 + z2 = 0
Therefore, for those conditions to be meet the magnitude of A must be equal to that of B.
b) Yes, Three or more vectors with different magnitudes can add up to zero.
For example, three forces acting at equilibrium like supporting the weight of a person with two different ropes.
W = T1 + T2
Where;
W = Weight
T1 = tension of wire 1
T2 = tension of wire 2
