Component Form of a Vector

The component form of a vector is a way to describe the vector using numbers that show its displacement in each direction. For vectors in two dimensions, it is written like a coordinate pair, but typically using braces instead of parenthesis. The x and y-values are known as the components of the vector.

The horizontal component is given by the difference between the x-value of the initial point and the x-value of the terminal point. Similarly, the vertical component is given by the difference between the y-value of the initial point and the y-value of the terminal point.

For vectors in three dimensions, three numbers are required to define a vector, so an additional component has to be incorporated. ⟨ x,y,z ⟩ Each component represents a displacement parallel to its corresponding axis.