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Math Help - Vectors

  1. #1
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    Vectors



    Could anyone help me to understand this question? I keep thinking that |u + v| = |u|+|v| in this scenario

    Thank you for your responses.
    Last edited by samstark; June 3rd 2011 at 04:13 PM.
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  2. #2
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    Quote Originally Posted by samstark View Post
    Could anyone help me to understand this question? I keep thinking that |u + v| = |u|+|v| in this scenario
    COME ON!
    That is not a question. It is a simple statement which is wrong.
    What is the question?
    What don't you understand?
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  3. #3
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    Quote Originally Posted by Plato View Post
    COME ON!
    That is not a question. It is a simple statement which is wrong.
    What is the question?
    What don't you understand?
    Sorry, the image I tried to post did not appear the first time. I edited my first post. I do not understand how the magnitude of the sum of the two vectors be less than the magnitude of each vector added up.
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  4. #4
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    Quote Originally Posted by samstark View Post
    Sorry, the image I tried to post did not appear the first time. I edited my first post.
    Well for any two vectors, \|\vec{U}+\vec{V}\|\le\|\vec{U}\|+\|\vec{V}\|
    That is the triangle inequality. That is a basic axiom for vectors.
    The sum of the lengths of two sides of a triangle is greater than the length of the third side.
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  5. #5
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    |\overrightarrow{u} + \overrightarrow{v}| Here you add the vectors together keeping the angle, so draw them from head(u) to toe(v) and look at them. If you did it correctly it should look like a roof or a ^ with a bigger angle. Then, draw a line from the start point of u to the end point of v. The new line is your |\overrightarrow{u} + \overrightarrow{v}| It should now look like a triangle

    In |\overrightarrow{u}| + |\overrightarrow{v}| you're just adding the total magnitude of the two vectors, so just draw the magnitude of vector v, and then continuing in a straight line draw the magnitude of vector u. Just add the vectors together in a straight line and call it |\overrightarrow{u}| + |\overrightarrow{v}|. Done correctly this would just look like a straight line.

    Look at what you drew, analyze it, and understand it's an exercise to get you to see why the triangle identity works. They just want you to draw it so that you can also conceptualize it in your mind. The idea is you'll learn the math language more intuitively and it's an opportunity to see why math works the way it does. Good luck!
    Last edited by Stro; June 3rd 2011 at 04:50 PM.
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  6. #6
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    The most fundamental concept here is "a straight line is the shortest distance between two points". The direct line from the base of u to the tip of v is a single straight line which is thus shorter than going from the base of u to the tip of u and then to the tip of v.
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