Exploring Vectors in 3 Dimensions
Drag the three points, A, B and C along their respective axes to manipulate the vector u. Click on the "Show Construction Lines" Button to display how the tip of the position vector is found. Note that you can hold the Shift Key and use the mouse wheel to zoom in and out if you want to try with higher numbers.
Note how the interception of the x and y coordinates are found using parallel lines, then moved "up" or "down" parallel to the z axis to find the tip of the vector. Drag the points and make note of how the orientation of the vector changes as different values are made negative.