Part 3: Vector Arithmetic
The parallelogram law (which we prove in the exercises) says that the sum u+v is the main diagonal of the parallelogram formed by u and v. In addition, the difference of 2 vectors is
u - v = u1-v1,u2-v2,u3-v3 ñ
which corresponds to the off-diagonal of the parallelogram defined by u and v.
If u = kv for some nonzero scalar k, then u and v are said to be scalar multiples of each other. Geometrically, if u and v are scalar multiples of each other, then u and v are said to be parallel.
EXAMPLE 6 Find u+v and 2v when u = 3,2 ñ and v = 0,-4 ñ
Solution: Their sum is given by
u+v = 3,2 ñ + 0,-4 ñ = 3+0,2-4 ñ = 3,-2 ñ
Moreover, multiplication of v = 0,-4 ñ by the scalar 2 yields
2v = 2 0,-4 ñ = 0,-8 ñ
Comment too long. Click
here to view the full text.
