Results 1 to 4 of 4

Math Help - vector dot product

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    97

    vector dot product

    Hello
    I have a question which I am not happy with

    Find the angle between a and b given

    |a|= 4
    |b|= 4
    and
    |a-b|= 7

    I have drawn it out and just got myself confused.
    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    Magnitude of (a-b) is given as

    R^2 = a^2 + b^2 - 2abcos(\theta)

    Substitute the values and find θ.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,245
    Thanks
    1
    Method I.
    Let \overrightarrow{a}=\overrightarrow{AB}, \ |\overrightarrow{a}|=|\overrightarrow{AB}|=AB=4

    \overrightarrow{b}=\overrightarrow{AC}, \ |\overrightarrow{b}|=|\overrightarrow{AC}|=AC=4

    Then \overrightarrow{a}-\overrightarrow{b}=\overrightarrow{AB}-\overrightarrow{AC}=\overrightarrow{CB}

    and |\overrightarrow{a}-\overrightarrow{b}|=|\overrightarrow{CB}|=CB=7

    So, \overrightarrow{a}, \ \overrightarrow{b}, \ \overrightarrow{a}-\overrightarrow{b} are the sides of the triangle ABC.

    From the cosine law we have

    \cos A=\displaystyle\frac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}=-\frac{17}{32}

    Method II
    |\overrightarrow{a}-\overrightarrow{b}|^2=(\overrightarrow{a}-\overrightarrow{b})^2=|\overrightarrow{a}|^2+|\ove  rrightarrow{b}|^2-2\cdot\overrightarrow{a}\cdot\overrightarrow{b}

    Then \overrightarrow{a}\cdot\overrightarrow{b}=-\displaystyle\frac{17}{2}

    Now, \cos\left(\widehat{\overrightarrow{a},\overrightar  row{b}}\right)=\displaystyle\frac{\overrightarrow{  a}\cdot\overrightarrow{b}}{|\overrightarrow{a}|\cd  ot|\overrightarrow{b}|}=-\frac{17}{32}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2009
    Posts
    97
    Thanks to both
    I shall have a go at this and come back if I am struggling
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: September 7th 2011, 05:31 PM
  2. Vector Product #2
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: March 4th 2011, 11:29 AM
  3. Vector Product
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 3rd 2010, 05:02 AM
  4. Replies: 6
    Last Post: September 7th 2010, 09:03 PM
  5. dot product of vector
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 19th 2008, 05:04 PM

Search Tags


/mathhelpforum @mathhelpforum