Can two vectors, of unequal magnitude, add up to give the zero vector? Can three unequal vectors? Under what condition?
No. Yes (when the sum of any two is equal and oppostite to the third)
Yes, two vectors of unequal magnitude can add up to give the zero vector. This occurs when the two vectors have the same direction but opposite magnitudes. Let's call these vectors A and B.
To obtain the zero vector by adding two vectors, the magnitudes of both vectors must be equal and their directions must be opposite. In other words, A = -B.
Similarly, three vectors of unequal magnitude can add up to give the zero vector. Let's call these vectors A, B, and C.
For three unequal vectors to add up to the zero vector, they must satisfy the condition that the sum of any two vectors cancels out the third vector. Mathematically, this can be expressed as A + B + C = 0.
This condition requires that the vectors form a closed triangle, known as a "closed polygon" or a "closed system." The three vectors must be arranged such that their resulting vector additions create a closed loop with no net displacement.