Concept Overview

In vector addition, the resultant is zero if the given vectors form a closed polygon when drawn head-to-tail.
For unequal and non-zero vectors, the smallest such combination occurs when three vectors form a closed triangle.

Option Analysis

Option a: Two

Two non-zero vectors can sum to zero only if they are equal in magnitude and opposite in direction.
If magnitudes differ, they cannot cancel each other completely, leaving a non-zero resultant.

Option b: Three (Correct)

Three unequal non-zero vectors can give a zero resultant when they form a closed triangle.
When placed head to tail, their vector sum equals zero, since:
A⃗ + B⃗ + C⃗ = 0

or equivalently,
C⃗ = −(A⃗ + B⃗).

Example: Vectors of magnitudes 3N, 4N, and 5N can satisfy this condition
if arranged at appropriate angles to form a closed triangle.

Option c: Four

Four unequal vectors can also result in zero resultant (for instance, forming a closed quadrilateral or a tetrahedral configuration),
but since three already suffice, three is considered the minimum number for the coplanar case.

Option d: Five

Five or more vectors can sum to zero, but they exceed the minimum necessary number.

Vector Addition Concept

Vectors add according to the parallelogram or polygonal law.
For a zero resultant, the vectors must form a closed polygon.
Unequal non-zero vectors cannot satisfy this condition with just two vectors,
but can with three that obey the triangle inequality (a + b > c, etc.).

Conclusion

Therefore, the minimum number of unequal non-zero vectors whose resultant is zero is three.