ACTIVITY 2.3
PARALLELOGRAM LAW

If we apply the parallelogram law to make sum of two given vector by his components, we also arrive to the conclusion that components must add the respective ones of each vector.

So in the figure we have it sum of the same previous activity vectors

+ = (1, 3) + (4, 2) = (1+ 4, 3+3) = (5, 5)
      + = (-1, -3) + (5, 2) = (-1+ 5,-3+2) = (4, -1)

Now made them using the parallelogram law now.

Also you check that if= (u _1, u ₂) and= (v ₁, v _2,) then

+ = (u _1, u ₂) + (v ₁, v ₂) = (u ₁ + v _1, u ₂ + v ₂)

INTERACTIVE ACTIVITY

You have the sum now+of two vectors which is obtained applying the parallelogram law.

Moving the green points to vary the vectorsand  , you make graphically next sums given vectors by his components:

1) (4, -2) + (2, 5)
2) (-3, 1) + (4,-7)
3)(0, -4) + (-6, 7)
4) (3, -3) + (-3, -3)
5) (5, 4) + (1,-4)
6) (-5, -3) + (5, 3)

You observe also that always it is verified:
              Components of (+) =
    Components of+ components of

SOLUTION

a) (5, 2) + (-2, 4)

d) (-3, 3) + (-3, 3)

b) (-7, 4) + (1, -3)

e) (-4, 1) + (4, 5)

c) (7, -6) + (-4,0)

f) (-3, 5) + (3, -5)

END OF ACTIVITY 2.3
PARALLELOGRAM LAW