My Math Forum Angle Between Two Vectors Proof - RARE

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top