What length restrictions are required for three
vectors to have a vector sum of zero? Explain your reasoning.
To have a vector sum of zero, the three vectors must form a closed triangle. This means that the sum of any two vectors must be equal in magnitude and opposite in direction to the third vector, canceling each other out when added together.
Mathematically, if we have three vectors A, B, and C, their vector sum is given by:
A + B + C = 0
If the vectors have different lengths, it would not be possible for them to form a closed triangle. One or more vectors would extend beyond the triangle formed by the other vectors and thus cannot be canceled out by the other vectors.
Therefore, to have a vector sum of zero, the length restrictions for the three vectors are that they must be of equal length.