School of Mathematics and Statistics, The University of Sydney
 7. Cartesian coordinates in three dimensions
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Length of a vector in terms of components

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The length of the vector -O-->Q in the XOY plane is V~ --2---2- x + y.

Y Q S y V~ x2-+-y2- y O x X R

From the three dimensional picture below,

Z T P = (x,y,z) k j z O y S Y xi R Q X

“cut out” the triangle OPQ to obtain:

P ------------ V~ x2 + y2 + z2 z V~ -------- O x2 + y2 Q

It can be seen that the length of the vector ---> OP is V~ ------------ OQ2 + QP 2 = V~ ------------ x2 + y2 + z2.

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Main menu Section menu   Previous section Next section Cartesian form of a vector Addition and subtraction of vectors in terms of components