Vectors!

Hello everyone,
I hope you all had a fantastic weekend!
It's my birthday today, just thought everyone would love to know that, haha :)
Anywayyyy, back to school tomorrow... already...

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>
vector multiplication: kv=k<a,b>=<ka,kb>

To find a vector from two points:
p2-p1

Vector equation:
(x,y)=(x0, y0)+t(a,b)

Parametic equations:
x=x0+at
y=y0+bt

absolute value of v= square root of x^2+y^2= magnitude of a vector

Example 1:
Give the component form of Ab and find the magnitude of AB.
A(1,-2), B(3,-2)
(3,-2)-(1,-2)= (3-1,-2+2) = <2,0> vector
square root of -4^2+-3^2= square root of 16+9= square root of 25 = 5 magnitude

Example 2:
Polar coordinates of point P are given and O is the origin.  Give its components.
P(6,72degrees)
x=6cos72= 1.854
y=6sin72= 5.706

Example 3:
Let u= (3,1) v= (-8,4) and w= (-6,-2).  Calculate each expression.
a. u+v
(3+-8, 1+4)
=<-5,5)
b. u-v
<3+8, 1-4>
=<11,-3>
c. 3u+w
<9,3> + <-6,-2>
=<3,1>