You remember that the subtraction - between two vectors and it is defined as the sum of the first of them with the opposite of the second: - = + (- ). It is easy to see that the components of - they are obtained changing the sign of components of , that is to say, if = (v 1, v 2), then - = (-v 1 ,-v 2). Then, it is arrived to the conclusion that to subtract two vectors is enough with subtracting his components:
- = + (- ) = (u 1, u 2) + (-v 1, -v 2) = (u 1- v 1, u 2- v 2)
Summarizing, the additions/subtractions of two vectors = (u 1,u 2) and = (v 1,v 2), when you work with components, they obtain so:
+ = (u 1 + v 1, u2 + v 2)
- + = (-u 1 + v 1, -u 2 + v 2)
- - = (-u 1 - v 1, -u 2 - v 2)
- = (u1 - v 1, u 2 - v 2)
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![](gif/sum_res.gif) |