Introduction:
In physics, vectors are quantities that have both magnitude and direction. They are represented graphically by arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector. In this question, we are given a vector of magnitude 10N, and we need to find its x-component and y-component.

Components of a Vector:
A vector can be resolved into two or more mutually perpendicular components. In a two-dimensional Cartesian coordinate system, a vector can be resolved into its x-component and y-component. The x-component represents the projection of the vector onto the x-axis, and the y-component represents the projection of the vector onto the y-axis.

Finding the x-component:
To find the x-component of a vector, we need to determine the magnitude of the projection of the vector onto the x-axis. This can be done by multiplying the magnitude of the vector by the cosine of the angle between the vector and the x-axis.

Let's assume the angle between the vector and the x-axis is θ. The x-component of the vector can be calculated using the formula:
x-component = magnitude * cos(θ)

In this case, we are not given the angle θ. However, since we are only interested in the x-component, we can assume that the vector lies along the x-axis, and therefore, the angle between the vector and the x-axis is 0 degrees. In this case, the x-component would be equal to the magnitude of the vector.

Therefore, the x-component of the vector is 10N.

Finding the y-component:
Similarly, to find the y-component of a vector, we need to determine the magnitude of the projection of the vector onto the y-axis. This can be done by multiplying the magnitude of the vector by the sine of the angle between the vector and the y-axis.

Let's assume the angle between the vector and the y-axis is φ. The y-component of the vector can be calculated using the formula:
y-component = magnitude * sin(φ)

In this case, we are not given the angle φ. However, since we are only interested in the y-component, we can assume that the vector lies along the y-axis, and therefore, the angle between the vector and the y-axis is 90 degrees. In this case, the y-component would be equal to the magnitude of the vector.

Therefore, the y-component of the vector is 10N.

Conclusion:
In conclusion, for a vector of magnitude 10N, the x-component is equal to 10N and the y-component is also equal to 10N. The x-component represents the projection of the vector onto the x-axis, while the y-component represents the projection of the vector onto the y-axis.