Find T,N and B for the curve r(t)=(3cos(4t),3sin(4t),4t) at the point t=0 Give your answers to two decimal places

Answer 1

T=r'/|r'|

r'=(-12sin4t,12cos4t,4)

|r'|=4/√10,,,,for all t

at t=0,,,T=(0,3/√10,1/√10)

minus sign correction

N=T'/|T'|

T'=((-12/√10)cos4t,(-12/√10)sin4t,0)

|T'|=12/√10,,,,for all t

at t=0 ,,,N=(-1,0,0)

B=TxN cross-product

B=((-1/√10)sin4t,(1/√10)cos4t,4/√10)

corrected

at t=0,,,B=(0,-1/√10,-3/√10)

see if this matches your calculations.