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so we have understood one more thing.....

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so we have understood one more thing.....

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reversing vectors means write them with opposite sign

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We do the same thing for the moltiplication

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We do the same thing for the moltiplication

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now, we try to understand how does COLUMN VECTORS work.

first of all, we must know that the upper number is the x one and the downer is the y number; we consider them number-by-number, so they are not fractions.

At the end we just add the two (x) numbers and the two (y) numbers

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now create a triangle OAB: le sum of a and b is the a+b

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now create a triangle OAB: le sum of a and b is the a+b

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replace vector b at the end or vector a (or vice versa)

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replace vector b at the end or vector a (or vice versa)

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if we consider the vectors a&b, we can...

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if we consider the vectors a&b, we can...

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so it isn't a vector

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how can I be sure that it has magnitude and direction?

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how can I be sure that it has magnitude and direction?

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now consider 5km

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east

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how can I be sure that it has magnitude and direction?

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how can I be sure that it has magnitude and direction?

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consider 5km east

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5km

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but we can consider more than a single vector.........

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but we can consider more than a single vector.........

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in this case, we have the vector a, which is (6;5). It's written as a COLUMN VECTOR

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A vector is a mathematical structure that has magnitude and direction. We can represent it on the CARTESIAN PLANE