Results 1 to 6 of 6

Math Help - Finding Unit Normal Vector

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    Finding Unit Normal Vector

    Alright, so here's a question from my online Calc 3 assignment. I know the formula for N(t), it is T'(t)/|T'(t)|. However I am still very stuck and confused as to how to find N. I can find B easily, it's just getting to N that is giving me problems.

    Find the vectors T, N, and B at the given point.
    .

    (I found T correctly, it was <6/19, 18/19, 1/19>.)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,346
    Thanks
    29
    Quote Originally Posted by melanie89 View Post
    Alright, so here's a question from my online Calc 3 assignment. I know the formula for N(t), it is T'(t)/|T'(t)|. However I am still very stuck and confused as to how to find N. I can find B easily, it's just getting to N that is giving me problems.




















    Find the vectors T, N, and B at the given point.

    .


    (I found T correctly, it was <6/19, 18/19, 1/19>.)
    \bold{r' } = < 2t, 2t^2,1> and

    || \bold{r' } || = \sqrt{4t^2 +4 t^4 + 1} = 2t^2+1

    so

    \bold{N} = \frac{< 2t, 2t^2,1>}{2t^2+1} = \left< \frac{2t}{2t^2+1} ,\frac{2t^2}{2t^2+1},\frac{1}{2t^2+1} \right>
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by danny arrigo View Post
    \bold{r' } = < 2t, 2t^2,1> and
    || \bold{r' } || = \sqrt{4t^2 +4 t^4 + 1} = 2t^2+1 so
    \bold{{\color{red}N}} = \frac{< 2t, 2t^2,1>}{2t^2+1} = \left< \frac{2t}{2t^2+1} ,\frac{2t^2}{2t^2+1},\frac{1}{2t^2+1} \right>
    You have found \bold{T} not \bold{N}

    \bold{N} = \frac{{T'}}<br />
{{\left\| T' \right\|}} = \frac{{r' \times \left( {r'' \times r'} \right)}}<br />
{{\left\| {r' \times \left( {r'' \times r'} \right)} \right\|}}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,346
    Thanks
    29
    Quote Originally Posted by Plato View Post
    You have found \bold{T} not \bold{N}

    \bold{N} = \frac{{T'}}<br />
{{\left\| T' \right\|}} = \frac{{r' \times \left( {r'' \times r'} \right)}}<br />
{{\left\| {r' \times \left( {r'' \times r'} \right)} \right\|}}
    Your absolutely right. I did stop short didn't I (and with a typo no doubt)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2009
    Posts
    2
    I found the correct N using the formula r' x (r'' x r') / |r' x (r'' x r')|. Thanks so much for your help!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2008
    Posts
    27
    My homework is almost identical to this except my point is <9, -18, -3>.
    I got the same T as you all did, except I'm not sure what to plug into it to get my point. I plugged in 9 for my x value but I got it wrong. I got 0.11. What am I doing wrong?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Unit Normal Vector
    Posted in the Calculus Forum
    Replies: 9
    Last Post: June 13th 2011, 06:04 AM
  2. Finding a unit normal vector
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 12th 2010, 10:24 AM
  3. unit normal vector
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 21st 2009, 07:59 AM
  4. show unit normal vector..
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 12th 2009, 06:22 PM
  5. Unit normal vector function
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 2nd 2008, 06:56 PM

Search Tags


/mathhelpforum @mathhelpforum