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13.4 HelixUnitTangent+UnitPrinNormalVectors 240924done
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and the Velocity Vector was:
and the Velocity Vector was:
14
Expression 15: vector left parenthesis, "P" , "P" plus "V" , right parenthesis
v
e
c
t
o
r
P
,
P
+
V
15
QUESTION: how will the Velocity Vector compare to the Unit Tangent Vector?
QUESTION: how will the Velocity Vector compare to the Unit Tangent Vector?
16
The POINT that is the head/end of Unit Tangent VECTOR when t = (pi)/2
The POINT that is the head/end of Unit Tangent VECTOR when t = (pi)/2
17
Expression 18: "T" equals left parenthesis, negative StartFraction, 1 Over StartRoot, 2 , EndRoot , EndFraction , 0 , StartFraction, 1 Over StartRoot, 2 , EndRoot , EndFraction , right parenthesis
T
=
−
1
2
,
0
,
1
2
18
and the Unit Tangent vector with the initial point at P is:
and the Unit Tangent vector with the initial point at P is:
19
Expression 20: vector left parenthesis, "P" , "P" plus "T" , right parenthesis
v
e
c
t
o
r
P
,
P
+
T
20
QUESTION: how will the Unit Tangent Vector compare to the Unit Principle Normal Vector?
QUESTION: how will the Unit Tangent Vector compare to the Unit Principle Normal Vector?
21
The POINT that is the head/end of Unit Principle Normal VECTOR when t = (pi)/2
The POINT that is the head/end of Unit Principle Normal VECTOR when t = (pi)/2
22
Expression 23: "N" equals left parenthesis, 0 , negative 1 , 0 , right parenthesis
N
=
0
,
−
1
,
0
23
and the Unit Principle Normal vector with initial point at P is:
and the Unit Principle Normal vector with initial point at P is:
24
Expression 25: vector left parenthesis, "P" , "P" positive "N" , right parenthesis
v
e
c
t
o
r
P
,
P
+
N
25
All done .
All done .
26
Expression 27: "V" equals left parenthesis, negative 1 , 0 , 1 , right parenthesis
V
=
−
1
,
0
,
1
27
Ignore this set-up folder (colors)
Ignore this set-up folder (colors)
Hide this folder from students.
28
35
powered by
powered by
"x"
x
"y"
y
"z"
z
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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