Question

What are the x- and y-components of vector eu of figure p3.8 in terms of the angle u and the magnitude e?

Answer 1

The x- and y-components of a vector with magnitude e and angle u from the x-axis are Ex = e cos(u) and Ey = e sin(u), respectively.

Step-by-step explanation:

The x- and y-components of a vector can be expressed in terms of the vector's magnitude and the angle it makes with a reference axis. For a vector with magnitude e and an angle u relative to the x-axis, the x-component (Ex) and the y-component (Ey) can be found using trigonometric relationships.

The x-component is Ex = e cos(u) and the y-component is Ey = e sin(u). These relationships come from the definition of cosine and sine in a right triangle or from the projection of the vector onto the respective axes.

For example, in a 45° right triangle, the components would be equal if the vector makes a 45° angle with the axis, since cos(45°) = sin(45°).

Answer 2

To find the x- and y-components of a vector, use the magnitude of the vector (e) and the angle (u) with the x-axis to calculate the components: Vx = e * cos(u) and Vy = e * sin(u).

Step-by-step explanation:

To express the x- and y-components of a vector in terms of its magnitude and direction (angle η), we can use trigonometric relationships. The x-component (Vx) of the vector is found by multiplying the magnitude of the vector (e) by the cosine of the angle (u), while the y-component (Vy) is found by multiplying the magnitude by the sine of the angle. These relationships originate from the fact that the x- and y-components represent the adjacent and opposite sides, respectively, of a right triangle formed by the vector and its components.

For example, if the magnitude of the vector is represented by e and the angle it makes with the x-axis is represented by η, the components are determined as follows:

• Vx = e * cos(η)
• Vy = e * sin(η)