Amy's Reflection #35

okay here is some stuff we learned this week..

Vector Operations with Coordinates
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)

The Dot Product
If v1 = (x1, y1) and v2 = (x2, y2) then the dot product, denoted by v1•v2 is defined by: v1•v2 = x1x2 + y1y2.

Properties of the Dot Product
1. u • v = v • u
2. u • u = |u|²
3. k(u • v) = (ku) • v
4. u • (v + w) = u • v + u • w

**if two vectors are orthogonal, the dot product=0

**if two vectors are parallel, then x2/x1=y2/y1

Mid point formula: (x1+x2/2, y1+y2/2, z1+z2/2)

Example:

1. u= (3,-6) v= (4,2) w= (-12, -6)

show that u&v are perpendicular and that v&w are parallel.

u . v= 3(4)+(-6)(2)=0

-12/4 = -6/2
-3 = -3

2. Find the midpoint of (2,2,2) and (2,4,6)

= 2+2/2, 2+4/2, 2+6/2

= (2, 3, 4)

okay i also need help in remembering some trig stuff so any review on anything would be appreciated..