12-1

12-2 Vectors
In this section on vectors, we learned how to do vector addition, subtraction, and scalar multiplication.  Also, we learned how to find a vector from two points, write a vector equation, and write a parametric equation.  We also covered how to find the absolute value of a vector and write an equation in component form.
- vector: slope
- vector addition: v+u = <a,b> + <c,d> = <a+c, b+d>
- vector subtraction: v-u = <a,b> - <c,d> = <a-c, b-d>
- scalar multiplication: kv = k<a,b> = <ka,kb>
- to find a vector from two points: P2 - P1
- vector equation: (x,y) = (xo, yo) + t<a+b> <---* (xo,yo) is the point, and (a,b) is the vector
- parametric equation: x = xo + at & y = yo + bt
- IvI = sq. root of x^2 + y^2 => magnitude of a vector
- component form: <rcos(theta),rsin(theta)>

Example 1: Given A(1,-2) and B(3,-2) find the a) component form b) absolute value of vector AB
a) P2 - P1
= (3-1,-2-1)
= <2,-4>


b) sq. root of 2^2 + (-4)^2
= sq. root of 20
= 2(sq. root of 5)


Example 2: If u = (1,1) and v = (2,4) find a) u+v b) u-v c) 2u-v
a) (1,1) + (2,4)
= <3,5>
b) (1,1) - (2,4)
= <-1,-3>
c) 2(1,1) - (2,4)
= (2,2) - (2,4)
= <0,-2>