Vector Contents

Components of Vectors

Any vector (e.g., F) in the x-y plane can be written as the sum of a vector along the + or - x direction and a vector along the + or - y direction. Mathematically, this is summarized as F=F_xî+F_yj, where F_x and F_y are the scalar components, and î and j are unit vectors -- vectors of length one along the positive x- and y-directions, respectively. Your task in this Illumination is to understand the relationship between the three vectors F, F_xî, and F_yj. Clicking "Go" reveals a random vector and the vectors along the x- and y-axes that add up to the original vector. To reduce the clutter, these vectors are labeled by the components F_x and F_y, but remember that the components must be multiplied by the î and j unit vectors to produce the actual vectors shown.