Results 1 to 3 of 3

Math Help - vectors and dot product in 3-d

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    26

    vectors and dot product in 3-d

    can someone tell me how to do this descriptively?
    Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
    A(0, 1, 1), B(-2, 4, 2), C(1, 1, -2),
    CAB = 115

    ABC = 29

    BCA = 3 36


    those are the correct answers....i dont think im picking the correct vertices when im doing them or im just retarded and completely missing how to do this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by ahawk1 View Post
    can someone tell me how to do this descriptively?
    Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
    A(0, 1, 1), B(-2, 4, 2), C(1, 1, -2),
    CAB = 115

    ABC = 29

    BCA = 3 36


    those are the correct answers....i dont think im picking the correct vertices when im doing them or im just retarded and completely missing how to do this.
    I will show you how to do one
    angle CAB

    First we need to find the vectors \vec{AC} \mbox{ and } \vec{AB}

    \vec{AC}=\vec i + -3 \vec k

    \vec{AB}=-2\vec i + 3\vec j+1 \vec k

    Now we can use the dot production to find the angle between two vectors

    \vec a \cdot \vec b =||a||||b||\cos(\theta)

    (-2-3)=(\sqrt{1^2+(-3)^2})(\sqrt{(-2)^2+(3)^2+(1)^2})\cos(\theta)
    \cos(\theta)=\frac{-5}{(\sqrt{10})(\sqrt{14})}

    \theta = \cos^{-1} \left( \frac{-5}{\sqrt{140}} \right) \approx 140^\circ

    This same method will work for the other two angles. Good luck
    Last edited by mr fantastic; April 25th 2009 at 05:15 PM. Reason: Fixed the last line of latex
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    635
    Hello, ahawk1!

    Find, correct to the nearest degree, the three angles of the triangle
    . . with the given vertices: . A(0, 1, 1),\quad B(-2, 4, 2),\quad C(1, 1, -2)

    Answers: . A = 115^o,\;\;B = 29^o,\;\;C = 36^o
    I would list all the vectors first . . .

    \begin{array}{ccc}\overrightarrow{AB} &=&\langle\text{-}2,3,1\rangle \\<br />
\overrightarrow{BA} &=& \langle 2,\text{-}3,\text{-}1\rangle \\<br />
|\overrightarrow{AB}| &=& \sqrt{14} \end{array} . . . \begin{array}{ccc}\overrightarrow{BC} &=& \langle 3,\text{-}3,\text{-}4\rangle \\<br />
\overrightarrow{CB} &=& \langle \text{-}3,3,4\rangle \\ |\overrightarrow{BC}| &=& \sqrt{34}\end{array} . . . \begin{array}{ccc}\overrightarrow{AC} &=&\langle 1,0,\text{-}3\rangle \\ \overrightarrow{CA} &=& \langle \text{-}1,0,3\rangle \\ |\overrightarrow{AC}| &=& \sqrt{10} \end{array}



    \cos A \;=\;\frac{AB\bullet AC}{|AB||AC|} \;=\;\frac{\langle\text{-}2,3,1\rangle\bullet\langle1,0,\text{-}3\rangle}{\sqrt{14}\sqrt{10}} \;=\;\frac{\text{-}2+0-3}{\sqrt{140}} \;= . \frac{\text{-}5}{2\sqrt{35}}\;=\;-0.422577127

    . . A \;=\;114.9973996^o \;\approx\;\boxed{115^o}



    \cos B \;=\;\frac{BA\bullet BC}{|BA||BC|} \;=\;\frac{\langle2,\text{-}3,\text{-}1\rangle\bullet\langle3,\text{-}3,\text{-}4\rangle}{\sqrt{14}\sqrt{34}} \;=\;\frac{6+9+4}{\sqrt{476}} \;=\;\frac{19}{2\sqrt{119}} \;= . 0.870863512

    . . B \;=\;29.44085226^o \;\approx\;\boxed{29^o}



    And: . C \;=\;180^o - 115^o - 29^o \;=\;\boxed{36^o}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Dot product of 2 vectors
    Posted in the Geometry Forum
    Replies: 4
    Last Post: September 28th 2011, 03:53 AM
  2. Replies: 1
    Last Post: May 14th 2008, 11:31 AM
  3. dot product and vectors.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 11th 2008, 02:04 AM
  4. Product Dot Vectors
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 21st 2008, 12:37 PM
  5. Vectors (Dot product?)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 6th 2008, 08:23 PM

Search Tags


/mathhelpforum @mathhelpforum