If two vectors have unequal magnitudes, can their sum be zero?

Two vectors with unequal magnitudes cannot have a sum of zero. Two vectors can only add up to zero if the sum of all components equal zero.

According to Buffalo State Physics, two vectors of unequal magnitudes cannot add up to zero. If two vectors A = ax + ay and B = bx + by are added together, the sum is (ax + ay) + (bx + by). To have a magnitude of zero, it requires (ax + ay) + (bx + by) = 0x + 0y. However, this only holds true if ax = -bx and ay = -by; therefore, the magnitudes of A and B must have the same positive value.