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Resultant Vector

The Resultant Vector

The final quantity you get when adding or subtracting vectors is called the resultant vector. In other words, the individual vectors can be replaced by the resultant – the overall effect is the same.

Definition: Resultant Vector

The resultant vector is the single vector whose effect is the same as the individual vectors acting together.

We can illustrate the concept of the resultant vector by considering our two situations in using forces to move the heavy box. In the first case (on the left), you and your friend are applying forces in the same direction. The resultant force will be the sum of your two applied forces in that direction. In the second case (on the right), the forces are applied in opposite directions. The resultant vector will again be the sum of your two applied forces, however after choosing a positive direction, one force will be positive and the other will be negative and the sign of the resultant force will just depend on which direction you chose as positive. For clarity look at the diagrams below.

Forces are applied in the same direction

(positive direction to the right)

f1f332911f35c24edd1a5ef015ecc5f4.png

Forces are applied in opposite directions

(positive direction to the right)

1f3edc853b638cbf0cec33138e2b8eb8.png

c04718e3f0c42b5e0d0708c231bcddb0.png

d42ecb418ab9712ae80db14b37536549.png

There is a special name for the vector which has the same magnitude as the resultant vector but the opposite direction: the equilibrant. If you add the resultant vector and the equilibrant vectors together, the answer is always zero because the equilibrant cancels the resultant out.

Definition: Equilibrant

The equilibrant is the vector which has the same magnitude but opposite direction to the resultant vector.

If you refer to the pictures of the heavy box before, the equilibrant forces for the two situations would look like:

1bc01a42b9d2bc3556c40c82dadbf79a.png

48d805d2ae872271f47b4fdcba6c7d0c.png

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