1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Area of a triangle (cross product lesson)

  1. Jul 16, 2014 #1
    1. The problem statement, all variables and given/known data

    Youtube: Lec 2 | MIT 18.02 Multivariable Calculus, Fall 2007 (Video time frame: between 11:00 minutes and 12:30 minutes)

    Find the area of a triangle.

    Area = [itex]\frac{1}{2}(base)(height)[/itex] = [itex]\frac{1}{2}|a||b|sinθ[/itex]

    The lecturer says to first find cosine of the angle using dot product. Next, solve for sine using [sin[itex]^{2}θ + cos^{2}θ[/itex] = 1]. And then substitute into area formula.

    However, he doesn't actually work this out, so I don't know what formula its supposed to produce or how to actually arrive there. This is a section on cross products so this might be a preface to the cross product formula and I'm interest to know where he was actually going with this. Any info would be very appreciated. Thanks.
     
  2. jcsd
  3. Jul 16, 2014 #2

    Nathanael

    User Avatar
    Homework Helper

    The magnitude of the cross product ([itex]\frac{1}{2}|a||b|sinθ[/itex]) is equal to the area of the parrallelagram made by the two vectors.

    This means the area of a triangle is equal to half of the magnitude of the cross product of two of the sides (with the third side being the diagonal of the parrallelgram which connects the ends of the first two sides)
     
  4. Jul 16, 2014 #3

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

     
  5. Sep 12, 2015 #4
    Thank you! Appreciate you guys
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Area of a triangle (cross product lesson)
  1. Area of this triangle (Replies: 3)

  2. Area of a triangle (Replies: 6)

  3. Area of triangle (Replies: 18)

  4. Area of this triangle? (Replies: 14)

  5. Area of a triangle (Replies: 2)

Loading...