Nathan's blog

So, we had a test on chapter 12 this past week, and i will just give you the notes and some examples from random sections.

Vectors have a magnitude and a direction.
To add vectors, you add head to tail. The triangle formed by the vectors give the resultant vector.

To add vectors algebraically, you add the components.
Scalar multiplication puts a scalar times each compound.

Parametric equations take only the x portion or y portion.

Dot product
-v1= (x1,y1) v2= (x2,y2)
-v1*v2= x1x2+y1y2

Dot product is a scalar product meaning it gives you a number.

Ex. If u=(3,6), v=(4,2) and w=(-12,-6). Find u*v and v*w. Show that u and v are perpendicular and v & w are parallel.

u*v=(3)(4)+(-6)(2)=0
v*w=(4)(-12)+(2)(-6)=-60

Since the dot product of u*v is 0, then they are perpendicular.

v=(4,2) w=(-12,-6)
v=2(2,1) w=-6(2,1)
V and W are parallel and multiples of each other.

That's it for chapter 12, im glad we're finished with it, because it was kinda hard.