Final answer:
To find a vector u parallel to the yz-plane, we need a vector with an x-component of zero. An example vector u could have the components (0, 1, 1), meaning it lies in the yz-plane with no displacement in the x-direction.
Step-by-step explanation:
To find a vector u that is parallel to the yz-plane, we should remember that any vector lying in the yz-plane will have an x-component of zero.
A vector parallel to the yz-plane can be expressed as u = (0, y, z), where y and z can be any real numbers. Let's use an example vector u with the components (0, 1, 1), which means it has no displacement in the x-direction (parallel to the yz-plane) and equal displacements in the y and z directions.
Step 1. Identify the x- and y-axes that will be used in the problem. We have the x-axis horizontal and the y-axis vertical. Here, the vector will have a zero x-component.
Step 2. Choose values for the y and z components, such as 1 for simplicity, to complete the vector: u = (0, 1, 1).
This vector u is indeed parallel to the yz-plane and has no component in the x-direction, fulfilling the requirement. Similar vectors can be found by setting the x-component to zero and choosing any real numbers for the y and z components.