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| PAGE: 866 | SET: Exercises | PROBLEM: 35 |
The vector function is 
and 
.
Principal unit normal vector: Let 
be the smooth curve represented by 
on an open
interval 
, If 
then principal unit normal vector is defined as, 
.
Where, 
is derivative of unit tangent vector defined as 
.
Find the unit tangent vector 
.
Consider .
Differentiate on each side with respect to 
.
Find the magnitude 
:
Substitute 
and 
values in
Substitute 
in above equation.
Unit tangent vector 
.
Apply derivative on each side with respect to .
Find the magnitude 
:
Principal unit vector .
Substitute corresponding values in above equation.
The vector function is .
.
.
Find 
:
At 
,
Find 
:
At ,
at is 
.
at is 
.
at is 
.
at is 
.
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