Question

find the unit tangent vector of

Answer 1

so for unit tangent vectors you will have to take the derivatives of each

Answer 2

i did that

Answer 3

i got r'= <1,x,x^2>

Answer 4

but i got confused when i put it over the absolute value

Answer 5

then you would need to get the magnitude

Answer 6

i know the formula is r'(x)/lr'(x)l

Answer 7

the magnitude i also got 1+x+x^2

Answer 8

okay. so you take each component and divided it by 1+x+x^2

Answer 9

so it would be <1/(1+x+x^2), x/(1+x+x^2), x^(1+x+x^2)> ?

Answer 10

the last component should be x^2/(1+x+x^2)

Answer 11

oh yeah thats what meant

Answer 12

but yes the unit tangent vector would be that

Answer 13

oh ok so i did the work correct i just got confused on the last step

Answer 14

thank you! i really appreciate your help

Answer 15

lol it happens

Answer 16

your welcome!

Answer 17

how would i find the unit normal vector?

Answer 18

i know i find the derivative of the solution

Answer 19

but do i do it one by one?

Answer 20

The normal vector is the same process as the tangent vector but instead of the original components you are going to use the tangent components

Answer 21

do i find the derivative/the magnitude for each one?

Answer 22

yes you do the derivative and magnitude of each tangent component

Answer 23

ok once im done finding it could i send u my solution and u tell me if its correct?

Answer 24

sure

Answer 25

how would i find the magnitude of it

Answer 26

for example the magnitude of 1/(1+x+x^2)

Answer 27

so for this portion, what is the derivative of 1/(1+x+x^2)

Answer 28

(-2x+1)/(x^2+x+1)^2

Answer 29

im sorry the numerator should be -(2x+1)

Answer 30

ok so the numerator looks good. So now just like how we found the magnitude for the tangental vector we would want to go through the same steps for the normal vector

Answer 31

wouldnt it be complicated to get the squareroot of the whole thing?

Answer 32

there is this website: http://www.ltcconline.net/greenl/courses/202/vectorFunctions/tannorm.htm

not sure how much help it will be. But essentially that is what you have to do