What Are Resultant Vectors?

A resultant vector is the result of either the addition, subtraction, multiplication, or division of two or more vectors to yield a new vector. This new vector is defined as the resultant vector. The calculator below performs the summation of two vectors, but other vector operations can be explored with the calculators linked below.

Resultant Vector Formula

The following formula is used to calculate the resultant vector from the summation of two different vectors.

X,Y,Z = X (vector 1) + X (vector 2), Y1 + Y2, Z1 + Z2

  • Where X, Y, and Z are the coordinate values of the new vector
  • X1,Y1,Z1 are the values of the first vector
  • X2,Y2,Z2 are the values of the second vector

Explained in words, this formula is the summation of each individual vector coordinate to yield 3 resultant coordinates of the new vector.

Subtraction of Resultant Vectors

In order to subtract two or more vectors, the same formula as above would be used, except each vector component would be subtracted from one another instead of added. For example, if vector 1 had an x-component of 3 and vector 2 had an x-component of 1, then the resultant vector from subtraction is 3-1 = 2.

Multiple Resultant Vectors

In some cases, there may be a situation in which the resultant vector of 3 or more vectors is required. In those cases, the formulas displayed above would just be adjusted to account for the additional coordinates.

For example, if there were 3 vectors that needed to be added together, the resultant vector would be the sum of each of the components. So if the x-component of the vector was 3,4 and 5 respectively, the sum of those would equal the new resultant vector x- component (3+4+5 = 12).

Uses of Resultant Vectors

Resultant vectors are most often used in physics to understand the combination of the values of 2 or more forces, velocities, or physical characteristics of matter. For example, when there are two or more forces acting on the same object, a single resultant vector can be used as an equivalent force as the two individual forces. This makes further calculations much more simple.

Resultant Vector Example

How to calculate a resultant vector?

  1. First, determine the values of the first vector.

    For this example problem, the values of the first vector are 10,13, and 3 for the x,y, and z coordinates of the vector respectively.

  2. Next, determine the values of the second vector.

    In this case, the second vector has values of 5,3, and 1 for the coordinates in the same order.

  3. Finally, calculate the resultant vector.

    Summing the individual vector components yields a new vector of:
    X = 10 + 5 = 15
    Y = 13 + 3 = 16
    Z = 3 + 1 = 4
    (15,16,4)

Resultant Vector Calculator

How to use the calculator:

Enter the values of two different vectors into the calculator. The calculator will evaluate and display the resultant vector.

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