How do you represent vector d in component form?

To represent vector d in component form, express it as d = (dx, dy) in 2D or d = (dx, dy, dz) in 3D.

In more detail, vectors are mathematical objects that have both magnitude and direction. When we talk about the component form of a vector, we are breaking it down into its individual parts along the coordinate axes. For a vector d in a two-dimensional space, we use the x-axis and y-axis. The component form of vector d is written as d = (dx, dy), where dx is the component along the x-axis and dy is the component along the y-axis.

If we are dealing with three-dimensional space, we also consider the z-axis. In this case, the component form of vector d is written as d = (dx, dy, dz), where dz is the component along the z-axis. These components can be thought of as the "steps" you take along each axis to get from the origin to the point represented by the vector.

For example, if vector d points from the origin (0,0) to the point (3, 4) in 2D space, its component form is d = (3, 4). This means you move 3 units along the x-axis and 4 units along the y-axis. Similarly, in 3D space, if vector d points to (3, 4, 5), its component form is d = (3, 4, 5), indicating movements of 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.

Understanding the component form of vectors is crucial for performing operations like addition, subtraction, and scalar multiplication, as it allows you to work with each dimension separately.