1. They form a closed triangle:
* If the three vectors are placed head-to-tail, they form a closed triangle. This means that the head of the third vector coincides with the tail of the first vector.
2. They are coplanar and satisfy the following conditions:
* Magnitude Condition: The magnitude of any one vector must be equal to the sum of the magnitudes of the other two vectors.
* Direction Condition: The direction of the vector with the largest magnitude must be opposite to the resultant of the other two vectors.
Example:
Imagine three forces acting on an object:
* Force A: 5 N to the right
* Force B: 3 N upwards
* Force C: 4 N downwards and to the left (such that its horizontal component is 3 N to the left)
If these forces are applied simultaneously, the object will remain stationary. This is because the sum of these three vectors is zero.
* Force A and Force B's horizontal components cancel out.
* Force B and Force C's vertical components cancel out.
In summary:
The sum of three vectors will be zero when they are arranged in a way that their components cancel each other out, either by forming a closed triangle or by satisfying the magnitude and direction conditions when they are coplanar.
