Next: Vector Algebra Up: Analytical vectors Previous: Notation and the components

Position vectors and displacement vectors

We are now free to deal with displacement and position vectors from an analytical viewpoint. The position vector to the general coordinate point (x,y,z) is usually written as tex2html_wrap_inline661 . This is a vector (called tex2html_wrap_inline663 which points from the origin to the point (x,y,z) and has a magnitude of tex2html_wrap_inline667 .)

A displacement vector from the point tex2html_wrap_inline669 to the point tex2html_wrap_inline671 has components tex2html_wrap_inline673 or can be written as tex2html_wrap_inline675 . This is a vector the ``starts at'' the first point (the one with the ``1'' subscripts) and points toward the second point. Notice that the magnitude of this vector is simply the actual Euclidian distance (the square root of the sum of the squares of the differences in the coordinates) between the two points.



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