L1 - 12.1 - Three Dimensional Coordinates - key - CALCULUS...

CALCULUS 3
NAME: ________________________________
LAB 1 12.1 THREE-DIMENSIONAL COORDINATES Lab Time: ____________ Date: ___________
Useful Formulas:
A point in three-dimensional rectangular coordinates is written as
 
z y x ,
The distance formula between two points
 
1 1
, , z y x
and
 
2 2 2
, , z y x
is:
     
2
1
2
1 2
2
1 2
z z y y x x d      
The midpoint between two points
 
1 1
, , z y x
and
 
2 2 2
, , z y x
is:
 
2 2
2 1 2 1 2 1
, ,
z z y y x x   
The equation for a circle with a center at
 
w v u , , and a radius of R is:
     
2
2 2 2
R w z v y u x    
1. Identify the point associated with each location:
,
1
2
1
2
 
A
F
C
G
E
B
D
H
2. In a coordinate plane labeled as follows:
If the positive x -axis is in the direction labeled u
and the positive y -axis is in the direction labeled m
then which direction is the positive z -axis
in a right-handed coordinate system?
,
,