The greatest possible resultant of two vectors can be achieved when they are in the same direction.

If two vectors have magnitudes 3 and 4, and they are in the same direction, their resultant will be the sum of their magnitudes, which is 3 + 4 = 7.

Therefore, the greatest possible resultant of two vectors of magnitude 3 and 4 is 7.

Maximum Resultant of Two Vectors: Magnitude 3 and 4

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