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а? а.b а. с a? ab cos y ac cos B = b. a b? b.c = ab cos y bc cos a С.а с.b с? ас cos B bc cosa = a?b°c² (1 – cos²a – cos?B – cosy +2 cos a cos B cos y)

а? а.b а. с a? ab cos y ac cos B = b. a b? b.c = ab cos y bc cos a С.а с.b с? ас cos B bc cosa = a?b°c² (1 – cos²a – cos?B – cosy +2 cos a cos B cos y)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 3E
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Show that the volume of a triclinic unit cell of sides a, b, and c and angles α, β, and γ is V = abc(1 − cos2α − cos2β − cos2γ + 2 cos α cos β cos γ)1/2 . 

 

There is this answered question already over here, but I have a dout regarding the process it took to get to the result, specifically, once we have our 3x3 matrix, how do we determine that this matrix equals to the linear eq? this is the image :D  

а2 а.b а. с a? ab cos y ac cos B bc cos a COS = b. a b? b.c = ab cos y С.а с.b с? ac cos B bc cos a = a²b?c? (1 - cos'a – cos?B – cos?y + 2 cos a cos B cos y)
Transcribed Image Text:а2 а.b а. с a? ab cos y ac cos B bc cos a COS = b. a b? b.c = ab cos y С.а с.b с? ac cos B bc cos a = a²b?c? (1 - cos'a – cos?B – cos?y + 2 cos a cos B cos y)
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