Vectors and Points 1

A vector is a directed line segment.

Vectors can be moved by parallel displacement. There is a one-to-one correspondence between vectors with their tails at the origin and points in the plane.

A point p with coordinates (x, y) corresponds to the vector V with head at (x, y) and tail at (0, 0). Move the vector V so that its tail is at the origin. Then double click to show the point.

You can explore further by moving V away from the origin - click on it and drag (if the axes come too, click again and drag). You can change the direction and length of V by dragging its head or tail. The copy of V at the origin dutifully changes right along.

Further explorations: Find a vector (tail not at the origin) which corresponds to the point (2, 1). Find one which corresponds to (1, -2). How many such vectors can you find? What is the relationship between the coordinates of the head and tail of V when not at the origin and the point corresponding to V? We'll take that up next.

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