MAC 2313 Lecture Notes - Unit Vector, Euclidean Geometry, Net Force
7 Oct 2013
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Document Summary
A vector has an initial point a and a terminal point b and is often represented symbolically in the form. Graphically vectors can be added, subtracted, and multi- plied by a scalar. For our purposes, an analytic formulation of a vector is re- quired in r3 (r2). This formulation is obtained by subtract- ing the coordinates of its initial point, a = (x0; y0; z0) from the coordinates of its terminal point, b = (x1; y1; z1), with the resulting vector represented as. Ab= x1 x0; y1 y0; z1 z0 : The magnitude or norm or length of the vector sented symbolically as | . Ab |, is given by the distance between its initial and terminal point using the formula. Example: find the representation and length of a vector with initial point (1; 2; 3) and terminal point (4; 0; 3). Example (cid:12)nd the length of the vector v = 3; 7; 1 :
