Resolving this vector into its x and y component vectors

Engineering
Thread starter AzureSekki
Start date Feb 22, 2020
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Component Vector Vectors

In summary, Resolving a vector into its x and y component vectors allows us to break down a single vector into its horizontal and vertical components, making calculations and analyses easier. The x component of a vector can be calculated by multiplying its magnitude by the cosine of its angle with the x-axis, while the y component can be calculated by multiplying its magnitude by the sine of its angle with the y-axis. A vector can only be resolved into two component vectors along orthogonal axes, as any additional components would not be perpendicular to these axes. The direction of the x and y components are determined by the x-axis and y-axis respectively, and it is possible to resolve a vector into non-orthogonal component vectors, although this is not as commonly used.

Feb 22, 2020

AzureSekki

Homework Statement: If R is the resultant of Forces P and Q. find p and q

Relevant Equations: R= P + Q
R = 360 lb
P = ?
Q = ?

Last edited by a moderator: Feb 24, 2020

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Feb 22, 2020

Lnewqban

Homework Helper

Gold Member

This is a case of subtraction of vectors.
Please, see:
https://www.varsitytutors.com/hotmath/hotmath_help/topics/adding-and-subtracting-vectors

Related to Resolving this vector into its x and y component vectors

1. What is the purpose of resolving a vector into its x and y component vectors?

The purpose of resolving a vector into its x and y component vectors is to break down a single vector into two separate components that are perpendicular to each other. This allows for easier analysis and calculation of the vector's magnitude and direction.

2. How do you calculate the x and y components of a vector?

To calculate the x and y components of a vector, you can use trigonometric functions such as sine and cosine. The x component is equal to the vector's magnitude multiplied by the cosine of the angle between the vector and the x-axis. The y component is equal to the vector's magnitude multiplied by the sine of the angle between the vector and the y-axis.

3. Can a vector have more than two component vectors?

No, a vector can only have two component vectors: one in the x-direction and one in the y-direction. This is because vectors are defined as having magnitude and direction, and adding more component vectors would change the magnitude and direction of the original vector.

4. How do you represent the x and y component vectors of a vector graphically?

The x and y component vectors of a vector can be represented graphically using a vector diagram. The x component vector is drawn as a horizontal line originating from the tail of the original vector, while the y component vector is drawn as a vertical line originating from the head of the x component vector. The original vector can then be drawn from the tail of the x component vector to the head of the y component vector.

5. What is the relationship between the x and y component vectors and the original vector?

The x and y component vectors, when added together, will result in the original vector. This means that the x and y component vectors are the two perpendicular components that make up the original vector. Additionally, the magnitude of the original vector can be calculated using the Pythagorean theorem by taking the square root of the sum of the squares of the x and y component vectors' magnitudes.