Results 1 to 5 of 5

Math Help - quick vector question

  1. #1
    Super Member
    Joined
    Dec 2008
    Posts
    509

    quick vector question

    Hi
    I need help on the following:

    Find the value of t that makes the angle between two vectors a=(3,1,0) and b(t,0,1) equal to 45 degrees.

    This is what i have done:

    a \cdot b = ab cos\theta

    \frac{a \cdot b}{ab} = 45

    \frac{3t}{\sqrt{10}\sqrt{t^2+1}} = 45

    45\sqrt{10(t^2+1)} = 3t

    \sqrt{10t^2 + 10} = \frac{3t}{45}

    10t^2 + 10 = \frac{t^2}{15^2}

    10t^2 + 10 = \frac{t^2}{225}

    225(10t^2 + 10) = t^2

    2250t^2 + 2250 = t^2

    2249t^2 = 2250

    t=\sqrt{\frac{2250}{2249}}

    t=1.00

    However the answer is  \frac{\sqrt{5}}{2}.

    P.S
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by Paymemoney View Post
    Hi
    I need help on the following:

    Find the value of t that makes the angle between two vectors a=(3,1,0) and b(t,0,1) equal to 45 degrees.

    This is what i have done:

    a \cdot b = ab cos\theta

    \color{red}{\frac{a \cdot b}{ab} = 45}

    \frac{3t}{\sqrt{10}\sqrt{t^2+1}} = 45

    45\sqrt{10(t^2+1)} = 3t

    \sqrt{10t^2 + 10} = \frac{3t}{45}

    10t^2 + 10 = \frac{t^2}{15^2}

    10t^2 + 10 = \frac{t^2}{225}

    225(10t^2 + 10) = t^2

    2250t^2 + 2250 = t^2

    2249t^2 = 2250

    t=\sqrt{\frac{2250}{2249}}

    t=1.00

    However the answer is  \frac{\sqrt{5}}{2}.

    P.S
    Dear Paymemoney,

    There is a mistake in the second line. Can you find it??
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2008
    Posts
    509
    is it suppose to be cos(45)??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2008
    Posts
    509
    found out my problem.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by Paymemoney View Post
    is it suppose to be cos(45)??
    Dear Paymemoney,

    Correct!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quick vector question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 12th 2010, 03:45 AM
  2. quick question vector fields
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 2nd 2009, 12:08 AM
  3. Quick vector question
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 7th 2009, 12:02 PM
  4. Quick Question about Vector Notation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 22nd 2009, 07:45 AM
  5. quick vector calc question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 21st 2009, 01:34 PM

Search Tags


/mathhelpforum @mathhelpforum