Hello Ernest D. Thank you very much for the last set of questions I have four more Vector Calculus questions all multiple choice. The answers are used as inputs for others, same as previous. Thanks...

Sol: (22) Given that,
     2cos sinr t i t j t k  
And
     ' 2sin cosr t i t j t  
Now,
 
 
 
2
0
2
2
0
2
0
2
0
. sin , 1, 2cos . 2sin , cos ,0
2sin cos
cos 2 1 cos
1
sin 2 sin
2
0 2 0
2
C
F dr t t t t dt
t t dt
t t dt
t t t






  
  
  
 
   
 
  
 
 


So...