12.1 – The Three Dimensional Coordinate System
•
The distance formula
o
=

+

+(

)
P1P2 x2 x1 y2 y1 z2 z1
Where
=(
,
,
)
P1
x1 y1 z1
and
=(
,
,
)
P2
x2 y2 z2
•
The Equation of a Sphere
o
(  ) +(  ) +(  ) =
x h 2 y k 2 z l 2 r2
o
Where (h,k,l) is the center of the sphere and r is the radius
•
Extra Exercises: Pg 797 #5, #7, #10, #13, #17, #25, #29,
o
12.2Vectors
•
Know how to add and subtract vectors geometrically and algebraically
•
The length of a vector (magnitude) can be determined by
o
=
+
a
a12 a22 a32
, where
=<
,
>
a1 a2 a3
•
Recall the problems of application of vectors using components
•
The standard basis vectors are <I,j,k>
•
Extra Exercises:
pg 805 #3,#9, #19, #29, #31
o
12.3Dot Product
•
The dot product of two vectors are
o
<
,
,
>
<
,
,
> =
+
+
a1 a2 a3
dot
b1 b2 b3
a1b1 a2b2 a3b3
•
Review the properties of the dot products on page 807
•
The geometric form of the dot product is
o
=
a dot b abcosθ
•
If the dot product of two vectors is zero then they are perpendicular, think cos
θ
•
Review the difference between scalar projections and vector projections
o
o
Scalar
o
Vector