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If
represents the vector displacement of point from the origin,
what is the distance between these two points? In other words, what is the length,
or magnitude, ,
of vector . It follows from a 3dimensional generalization of
Pythagoras' theorem that

(35) 
Note that if
then

(36) 
In other words, the magnitudes of vectors cannot, in general, be added
algebraically. The only exception to this rule (represented by the equality sign in the
above expression) occurs when the vectors in question all point in the same direction.
According to inequality (36), if we move 1m to the North (say) and next move
1m to the West (say) then, although we have moved a total distance of 2m, our net distance
from the starting point is less than 2mof course, this is just common sense.
Next: Scalar multiplication
Up: Motion in 3 dimensions
Previous: Vector addition
Richard Fitzpatrick
20060202