Q:

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

A:

Quick Answer

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.

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Full Answer

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.

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