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Homework Help: Area of triangle formed by 2 vectors

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data
    I have a triangle ABC formed by vectors a = ( 2, 10, 25 ) and b = ( 5, 4, -2 ) attached at a point P.
    And I have to calculate the area of the triangle ABC.


    2. Relevant equations
    I'm pretty certain that I need to find the area of the parellogram and then half it.
    So I need to find the cross product, by calculating the determinant.


    3. The attempt at a solution
    Calculating the determinant I got
    -120 i + 129 j - 42 k
    so does this mean i square those and take the square root of them to find the area of the parellogram and then half it...
    = 181.121
    => area of triangle = 90.56
     
  2. jcsd
  3. Apr 24, 2010 #2

    Dick

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    Sure, you're doing it right.
     
  4. Apr 24, 2010 #3
    Thanks..I thought I was on the right lines, just needed reassuring :)

    I got the area of the traingle to be 81root5 / 2

    But now I need to calculate the length of the height PM (where PM perpendicular to BC and the point M belongs to the line BC)

    I'm guessing as I know the area and 2 vectors I can take it from there...but I really have no idea....
     
  5. Apr 24, 2010 #4

    Dick

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    Use |axb|=|a|*|b|*sin(t), where t is the smaller angle between the vectors a and b. Find t and use trig.
     
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