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Answer :
To get a resultant of 7 meters, vectors are added in the same direction; for 1 meter, they are in opposite directions, and for 5 meters, they are at a right angle to each other. The answer is option C, 5m.
To obtain a resultant vector with a magnitude of 7 meters when combining two displacement vectors with magnitudes of 3 meters and 4 meters, the vectors must be added head-to-tail in the same direction. This is because vector quantities not only have magnitude but also direction, and when added in the same direction, their magnitudes sum up directly.
The magnitude of the resultant vector will be 1 meter if the two vectors are added head-to-tail but in exactly opposite directions. Here, the larger vector (4 meters) will essentially be subtracted by the smaller vector (3 meters) due to the opposite direction, yielding the difference as the resultant.
To achieve a resultant vector with a magnitude of 5 meters, the two vectors must be placed at a right angle (90 degrees) to each other. By using the Pythagorean theorem, because the original vectors form the legs of a right-angled triangle, it can be proven that the hypotenuse (resultant vector) will be 5 meters.
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