Monday, 27 July 2015

Proof of law of cosines using dot product

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  http://www.kurzweilai.net/the-law-of-accelerating-returns
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  http://17calculus.com/derivatives/product-rule/
If we had multiplied out first and there were factors other than a single x term, they would have been difficult to see in the completely multiplied out form. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject

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  http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-1-dot-product/
So, I have my vector, A, and if I have my vector, B, and I have some angle between them, I multiply the length of A times the length of B times the cosine of that angle. I know it sounds completely obvious from the definition here, but in the middle of the action when you're going to do complicated problems, it's sometimes easy to forget

Dot Product Basics


  http://www.math.washington.edu/~king/coursedir/m445w04/notes/vector/dotproduct.html
In the plane or 3-space, the Pythagorean theorem tells us that the distance from O to A, which we think of as the length of vector OA, (or just length of A), is the square root of this number. Dot Product Basics Dot Product Basics Dot Product of Two Vectors The dot product of two vectors A and B is a key operation in using vectors in geometry

  http://tutorial.math.lamar.edu/Classes/CalcII/DotProduct.aspx
Note as well that while the sketch of the two vectors in the proof is for two dimensional vectors the theorem is valid for vectors of any dimension (as long as they have the same dimension of course). Alternatively, you can also view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part

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