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Homework Help: A vector question (Proof)

  1. Oct 29, 2012 #1
    I am new at this forum. Firstly, I want to say I am happy to be a member of this forum. English is not my native language. So I can make some grammer and other mistakes. I try to write with no mistakes. If I make mistakes for writing, I apologize.
    I have a question. You see a triangle in the picture. There are some vectors. h is height or short distance between p0 and V3. In the picture, you see an equation to find h. How do you prove this equation?
  2. jcsd
  3. Oct 29, 2012 #2

    Simon Bridge

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    Welcome to PF;
    Have you tried starting with the definition of a vector cross-product?
  4. Oct 30, 2012 #3
    Thanks. Yes, I have. But I can't solve it.
    h is norm of short distance between p0 and V3. So I have to use a new symbol for short distance. I want to call it as V4.
    I have tried something but I have no idea. Some clues are very useful to prove this equation.
  5. Oct 30, 2012 #4
    What does [itex]h |V_{3}|[/itex] give you?
    What does [itex]|V_{1} \times V_{2}|[/itex] give you?
    It is related to a property of the triangle.
  6. Oct 30, 2012 #5
    Thanks but I do not have any idea.
  7. Oct 30, 2012 #6
    Okay, I'll be a little more explicit: how would you go about finding the area of the triangle? There are two ways: 1st is by geometrical means, and 2nd by vectorial methods.
  8. Oct 30, 2012 #7
    Ok. First way is not problem to find area of the triangle. But I do not know how to find area of the triangle with vectorial methods. I think second way is necessary to prove this equation. Thanks for your clues. But I need more than them.
  9. Oct 30, 2012 #8
    If A and B are the lengths of two sides of a triangle, and θ is the angle between the two sides, what is the equation for the area of the triangle in terms of A, B, and θ?
  10. Oct 31, 2012 #9
    Your clue is very helpful for me. Thanks. It is very easy now.
    Area of triangle (1/2)h|V3|sin900=(1/2)|V1||V2|sinθ
    Thank you everybody for your helping.
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