By Allen D. Bragdon

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If PB it and B are in inverse into which the should so happen that externally, the ratio A P / PE ratio A B is line P divided would be nega and the signs of m and n would be opposite, but the formula would hold without change if this difference of sign in m and n be taken into account. tive, Example 2 : To find the point of intersection of the medians of a triangle. at random. Choose the origin Let A BC be the given = A, ()B = B, and "00 = C. Let A ,C triangle. Let 0~A be respectively the middle points of the sides opposite the f , M vertices A, B, (7.

A= if and is written Thus A = 0. All null vectors are regarded as equal to each other without any considerations of direction. In fact a null vector from a geometrical standpoint would that is to be represented by a linear segment of length zero a It would have a consequently wholly inde point. say, by terminate direction or, what amounts to the same thing, none at be regarded as the limit approached by a If, however, vector of finite length, it might be considered to have that it all. direction which finite vector, is the limit approached by the direction of the the length decreases indefinitely and ap when proaches zero as a limit.

The sign is positive Any when b and a have the same direction have opposite directions. If then ; OA = negative, when they a, the vector r drawn ADDITION AND SCALAR MULTIPLICATION from the origin either direction any point of the to line A produced in is r = x a. (1) x be a variable scalar parameter this equation If 15 there may fore be regarded as the (vector) equation of all points in the B Let now be any point not that line produced the line or upon in either direction (Fig. 5). OA. line OA Let OB = b.