What is the maximum number of unequal vectors to result into a null vector ? Explain with the help of diagram.
Answers
The answer is 1 (or 0), or 2, or 3.
First, there is the trivial solution: the null vector by itself clearly “sums” to the null vector. (And, if you allow empty sums, then the empty set also sums to the null vector, so the answer would be that you need zero vectors.)
And now for the non-trivial answers.
If by “unequal vectors” you mean vector inequality, then the minimum is two: any non-zero vector and its negation are unequal and sum to the null vector.
However, if by “unequal vectors” you mean “vectors of unequal magnitude”, then the minimum is three: just use the length and orientation of the sides of any scalene triangle to form three vectors that sum to zero. (This works in reverse as well: any three vectors of unequal magnitudes which sum to the null vector will form a scalene triangle when placed head-to-tail in any order.) If you weaken the requirement to be that not all vectors have the same magnitude (but pair-wise, some of the vectors might be equal), then you can also use isosceles triangles (but not equilateral triangles).