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Unformatted text preview: A very important process in Mathematics is the search for the essence of objects, so that we shall not be hindered by the complicated nature of the objects. When we learnt counting of objects, it does not matter whether we count 3 apples and 4 apples or 3 oranges and 4 oranges. The importance is 3 and 4 and the total is 3 + 4 = 7. Similarly, it does not matter whether we are handling displacements, velocities or forces. We can due with them by using quantities which are described by lengths and directions. From the above theorem, why cannot we push a further step? Let us forget about the magnitude and direction for the time being and pay attention only to the components. We then can define a mathematics structure call R2, which is the set of 2—vectors with addition and multiplication by a scalar defined by — for any (:1) , (21) E R2 and A E R 2 2 IF—h‘x 99 bar—- \._____./ y + flfl 9;: a“? Nil—I Lop—n x.._____./\...____./ || || raw/fix ivyfifl gator—I MI—l ++ Uta“? -m.—~ \‘I—F/ 93 I: 51. ...
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