What is the difference between components and resultants

We very often need to separate a vector into perpendicular components. For example, given a vector like A in Figure 1, we may wish to find which two perpendicular vectors, A x and A y , add to produce it.

Figure 1. The vector A, with its tail at the origin of an x, y-coordinate system, is shown together with its x- and y-components, A x and A y. These vectors form a right triangle. The analytical relationships among these vectors are summarized below.

A x and A y are defined to be the components of A along the x — and y -axes. The three vectors A , A x , and A y form a right triangle:. Note that this relationship between vector components and the resultant vector holds only for vector quantities which include both magnitude and direction.

The relationship does not apply for the magnitudes alone. However, it is not true that the sum of the magnitudes of the vectors is also equal. That is,. To find A x and A y , its x — and y -components, we use the following relationships for a right triangle. Figure 2. Suppose, for example, that A is the vector representing the total displacement of the person walking in a city considered in Kinematics in Two Dimensions: An Introduction and Vector Addition and Subtraction: Graphical Methods.

Figure 3. If the perpendicular components A x and A y of a vector A are known, then A can also be found analytically. Figure 4. The magnitude and direction of the resultant vector can be determined once the horizontal and vertical components A x and A y have been determined.

To see how to add vectors using perpendicular components, consider Figure 5, in which the vectors A and B are added to produce the resultant R. Figure 5. Vectors A and B are two legs of a walk, and R is the resultant or total displacement. You can use analytical methods to determine the magnitude and direction of R.

If A and B represent two legs of a walk two displacements , then R is the total displacement. The person taking the walk ends up at the tip of R.

There are many ways to arrive at the same point. In particular, the person could have walked first in the x -direction and then in the y -direction. Those paths are the x — and y -components of the resultant, R x and R y.

When you use the analytical method of vector addition, you can determine the components or the magnitude and direction of a vector.

Step 1. Identify the x- and y-axes that will be used in the problem. Then, find the components of each vector to be added along the chosen perpendicular axes. Figure 6. To add vectors A and B, first determine the horizontal and vertical components of each vector. These are the dotted vectors A x , A y , B x and B y shown in the image.

Step 2. Find the components of the resultant along each axis by adding the components of the individual vectors along that axis. That is, as shown in Figure 7,.

Figure 7. The magnitude of the vectors A x and B x add to give the magnitude R x of the resultant vector in the horizontal direction. Similarly, the magnitudes of the vectors A x and B y add to give the magnitude R y of the resultant vector in the vertical direction. Components along the same axis, say the x -axis, are vectors along the same line and, thus, can be added to one another like ordinary numbers.

The same is true for components along the y -axis. For example, a 9-block eastward walk could be taken in two legs, the first 3 blocks east and the second 6 blocks east, for a total of 9, because they are along the same direction. So resolving vectors into components along common axes makes it easier to add them.

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The sum or difference of p and q is the of the x-term in the trinomial. A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials. J's study guide 1 card. What is the name of Steve on minecraft's name. Steel Tip Darts Out Chart 96 cards. Q: What is the difference between a resultant vector and a component vector? Write your answer Related questions. What is difference in resultant vector and vector resolution? What is the difference between resultant and equilibrant vector?

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The above discussion pertains to the result of adding displacement vectors. When displacement vectors are added, the result is a resultant displacement. But any two vectors can be added as long as they are the same vector quantity. If two or more velocity vectors are added, then the result is a resultant velocity. If two or more force vectors are added, then the result is a resultant force.

If two or more momentum vectors are added, then the result is In all such cases, the resultant vector whether a displacement vector, force vector, velocity vector, etc. The football player experiences three different applied forces. Each applied force contributes to a total or resulting force.