ACTIVITY 2.6
ADDING AND SUBTRACTING VECTORS

You remember that the subtraction-between two vectorsandit 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)

INTERACTIVE ACTIVITY

You have two vectors andand the vectors,

  +
- +
- -
  -

You can move the extremes of the vectorsand. You move them in many forms and you observe how additions and subtractions of two vectorandbehave.

Each vector goes along with his components. You check how components obtains of+, -+,  -- and- from the components ofand.

SOLUTION (Animation)

They give you the vectors

END OF ACTIVITY 2.6
ADDING AND SUBTRACTING VECTORS