Three mutually perpendicular steel panels meet along the x, y and z coordinate axes, which are so labeled at their outer ends. Three telescoping antennas with magnetic bases act as markers for the three components of a vector whose tail is at the origin. You can extend a fourth antenna, attached at the origin, to the point where the three component vectors meet.

Demonstration 04.09 -- Vector models, illustrates the concept of a vector – a quantity that has both a magnitude and a direction. Its web page shows how we represent vectors (either by magnitude and direction, or by their components), how we add or subtract them (to or from each other), and a few ways of multiplying them, either by a scalar or by each other. This 3-D vector board allows you to show graphically a vector in three dimensions, with its components. If we call our vector r, then its components are r_xi, r_yj and r_zk, where i, j and k are unit vectors pointing in the positive x, y and z directions, respectively, and we may write it as r = r_xi + r_yj + r_zk. The length of the red antenna, which parallels the x-axis, determines r_x, the length of the green antenna, which parallels the y-axis, determines r_y, and the length of the black antenna, which parallels the z-axis, determines r_z. To make a vector, you must set each antenna to whatever length you desire for the component it represents, then place them so that each pair of antennas is the same distance from the origin along the third axis, as the component that corresponds to that axis. In the example in the photograph, the x component is 4.5i, the y component is 5j, and the z component is 6k. Thus, the bases for the y and z components are both 4.5 units from the origin along the x axis, the bases for the x and z components are both 5 units from the origin along the y axis, and the x and y components are both 6 units from the origin along the z axis. When placed this way, the heads of the three components meet at a common point, which is where the head is, of the vector whose tail is at the origin, and which is composed of these three components. (This is equivalent to placing the tail of any component at the origin, then adding the other two, in turn; the resultant is the same.)