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Position vectors

The easiest type of vector to visualize is a position vector. This is a vector that is associated with a specific point. It has a magnitude, or length, equal to the distance from the origin to the point, and it has a direction that points straight from the origin to the point. Consider the vector drawn below.

This vector points three units to the right (along the +x axis) and four units up (along the +y axis). It points directly from the origin to the point (3,4), has a length of tex2html_wrap_inline555 and lies at an angle of tex2html_wrap_inline557 radians above the x axis. Since the vector and the point are essentially the same thing, one way we write this vector is by identifying it with the point (3,4) and say that the vector tex2html_wrap_inline521 is the same as the ordered pair (3,4). This is simply one way of saying that the vector tex2html_wrap_inline521 points three units to the right and four units up.



Vector Calculus
Mon Jul 14 10:10:30 MST 1997