ACTIVITY 2.4
ASOCIATIVITY OF THE ADDITION

In this activity we will prove the asociativity of the vector sum working with components.

If= (a ₁, a ₂), = (b ₁, b ₂)  and= (c ₁, c ₂), then

(+) + = [(a _1, a ₂) + (b ₁, b ₂)] + (c ₁, c ₂)
                          = (a₁ +b ₁ to ₂ +b _2,) + (c ₁, c ₂)
                          = (a ₁ +b ₁ +c ₁ to ₂ +b _2, +c ₂)
                          = (a ₁ a ₂) +, (b ₁ +c ₁, b ₂ +c ₂)
                          = (a ₁ a ₂) +, [(b ₁, b ₂) + (c ₁, c ₂)]
                          =++)

You observe that the demonstration that we have made is based on in the asociativity of the number sum.

INTERACTIVE ACTIVITY

This construction demonstrates that the vectors
(+) + and+ (+) always coincide.

You can move the green points and with them the vectors,and. To convince you.

You move them in a lot of forms and you observe that it always verifies

(+) + =+ (+)

You check the components of vectors,,,
+,+ and++. Also you verify this identity.

SOLUTION

1)  (+) +

3)  (+) +

END OF ACTIVITY 2.4
ASOCIATIVITY OF THE ADDITION