Question

find components of the vector in the new coordinate system characterized by the unit vectors of the new coordinate system rotated about the zaxis counterclockwise by π/4 radians

Answer 1

To find the new components of a vector in a rotated coordinate system by π/4 radians about the z-axis, apply the corresponding rotation matrix to the original vector components.

Step-by-step explanation:

The question involves finding the components of a vector in a rotated coordinate system, specifically one rotated counterclockwise by π/4 radians about the z-axis. To find the new components, you will need to apply a rotation matrix to the original vector components.

Step-by-Step Method:

1. Identify the initial vector components along the x, y, and z axes as x(t), y(t), and z(t) respectively.
2. Construct the rotation matrix for a rotation by π/4 radians counterclockwise about the z-axis:
3. Multiply the initial vector components by the rotation matrix to find the new rotated components.

Keep in mind that vector addition in the context of physics often refers to adding vector components along common axes, which simplifies the process of finding resultant vectors.