ACTIVITY 3.6
MODULE OF THE ADDITION OF TWO VECTORS

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Which relation exists between the module of addition of two vectors+and the modules of the vectorsand? That is, which relation exists between  |+| and || and ||?

The observation of a geometric sum vector brings us to the conclusion of
                                               |+| || +||
An observation more thoroughly of the geometric sum of two vectors let us that
                                               |+|  || +||
this inequality it is called triangular inequality, it is deduced of the fact of a side of a triangle is always minor than the sum of the other sides. Only if the two vectorsandhave the same direction and it  verifies |+| =|| +||.

If you know the two vector components= (u1, u2) and= (v1, v 2) , you can obtain the module of the sum+effecting the sum firstly
                                   + = (u 1, u 2) + (v 1, v 2) = (u 1 + v 1, u 2 + v 2)
And calculating the module later
                                           

INTERACTIVE ACTIVITY

a) You try to find, moving the green points if it seems convenient, any relation between the module of the sum+ and the modules of the adding and.

b) ¿ Is there any situation in which

|+| =|| +||

(That is to say, that the module of the sum is similar to the sum of the modules?) Try to find it moving the green points.

SOLUTION

HOMEWORK
(Do you want a Word document prepared for making this work?)

a) Check the triangular inequality with vectors= (3,4)  and= (12,5). That is to say, calculate || and ||, you calculate later+and his module |+| ; finally, you compare the three modules ||,  ||  and |+|.

b) Checks the triangular inequality with vectors= (2, -2)  and= (-3,1.)

END OF ACTIVITY 3.6
MODULE OF THE ADDITION OF TWO VECTORS

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