If the sum of their components in any two orthogonal directions is zero, the resultant is zero.
Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
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Take any three vectors in a plane which, when placed end-to-end form a triangle. The resultant of the three vectors will be zero.
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
Yes, it is possible to add three vectors of equal magnitude but different directions to get a zero vector. This occurs when the vectors are arranged in a way that their directions cancel each other out. Mathematically, this can happen when the vectors form a closed triangle or when they are evenly spaced around a circle.