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 April 24th, 2014, 09:28 AM #1 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Angle Between Two Vectors Proof - RARE Created this video to help prove why the equation below is correct: Did not find this proof in any text book and came across it by accident when trying to solve a vector problem. Everything just fell into place. You probably won't find this proof in any a level text book in the UK. Here is a latex version of the proof to use whilst you're watching the video: $\displaystyle 2ab\cdot cosC={ a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 }\\ \\ 2ab\cdot cos\theta ={ a }^{ 2 }+{ b }^{ 2 }-{ c }^{ 2 }\\ \\ but\quad a=\left| \underline { b } \right| ,\quad b=\left| \underline { a } \right| ,\quad c=\left| \underline { b } -\underline { a } \right| \\ \\ \therefore \quad 2\left| \underline { a } \right| \left| \underline { b } \right| \cdot cos\theta ={ \left| \underline { a } \right| }^{ 2 }+{ \left| \underline { b } \right| }^{ 2 }-{ \left| \underline { b } -\underline { a } \right| }^{ 2 }\\ \\ \therefore \quad 2\left| \underline { a } \right| \left| \underline { b } \right| \cdot cos\theta =\underline { a } \cdot \underline { a } +\underline { b } \cdot \underline { b } -\left[ \left( \underline { b } -\underline { a } \right) \left( \underline { b } -\underline { a } \right) \right] \\ \\ \therefore \quad 2\left| \underline { a } \right| \left| \underline { b } \right| \cdot cos\theta =\underline { a } \cdot \underline { a } +\underline { b } \cdot \underline { b } -\underline { a } \cdot \underline { a } -\underline { b } \cdot \underline { b } +2\underline { a } \cdot \underline { b } \\ \\ \therefore \quad 2\left| \underline { a } \right| \left| \underline { b } \right| \cdot cos\theta =2\underline { a } \cdot \underline { b } \\ \\ \therefore \quad \underline { a } \cdot \underline { b } =\quad \left| \underline { a } \right| \left| \underline { b } \right| \cdot cos\theta$ April 24th, 2014, 10:07 AM #2 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Attachment URL.... https://drive.google.com/file/d/0B-J...it?usp=sharing Last edited by perfect_world; April 24th, 2014 at 10:10 AM. Tags angle, proof, rare, vectors Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Rejjy Calculus 2 October 18th, 2012 01:06 PM 1love Calculus 1 May 24th, 2012 10:08 AM tony873004 Algebra 1 July 19th, 2011 02:46 PM Keysle Algebra 2 May 24th, 2011 05:06 AM AlexC Calculus 2 September 11th, 2007 07:57 AM

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