Vector Algebra

I.  Quiz

II.  Homework

III. Algebra of Vectors

If v = <a,b> and  w = <c,d> and k is a constant, then

v + w = <a + c,b + d>

kv = <ka,kb>

Example

3<2,1>  -  2<-1,3> = <6 + 2,3 - 3> = <8,0> = 8i

Geometrically v+w is the vector that corresponds to the diagonal of the parallelogram with two sides v and w.

The appropriate diagram will be drawn to show how v-w = v + (-w).

IV. Properties of Vector Addition and Subtraction

We have the following four properties of vectors:  If u, v ,and w are vectors and a and b are numbers then

1)  (u + v)  + w = u + (v + w)

2)  a(u + v) = au + av

3)  a(bv) = (ab)v

4)  u + v = v + u