operations with vectors

To add two vectors, u and v, we join the extreme of u with the origin of v and then, u + v has the origin of u as its origin and the extreme of v as its extreme. The coordinates are the addition of their coordinates.

Example: (2,2) + (5,2) = (7,4)

The opposite of a vector v, is another vector, -v, with the same magnitude and direction but opposite sense. The coordinates are the opposite of v-coordinates.

Example: if v(3,-1), then -v = (-3,1)

To subtract two vectors, u and v, we add u and –v. The coordinates are the subtraction of their coordinates.

Example: (2,3)-(4,1) = (-2,2)

The multiplication of a vector v by a scalar λ (λЄR), is another vector, λv, with:
- magnitude:|λ|·|v|
- the same direction with the same sense if λ>0, and opposite sense if λ<0.
The coordinates are the v-coordinates λ times.

Example: if v(3,-1), then -3v = (-9,3)

Exercise: If u(3,-2), v(-3,3), calculate:

a) u + v

b) u - v

c) -4u

Solutions:a) (0,1); b) (6,-5); c) (-12,8)