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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: TrueTears on December 22, 2008, 12:34:57 am

Title: angle vector questions
Post by: TrueTears on December 22, 2008, 12:34:57 am: 1. Show that, if a vector in three dimensions makes angles a, b , c respectively with the x, y, z axes, then cos^2a + cos^2b + cos^2c = 1
Title: Re: angle vector questions
Post by: :) on February 07, 2009, 11:18:38 pm: I was also wondering how to do this question, anyone?
Title: Re: angle vector questions
Post by: Mao on February 07, 2009, 11:29:01 pm: (x,y,z) has a modulus of $r=\sqrt{x^2+y^2+z^2}$

then, $(x,y,z) = (r\cos a, r\cos b, r\cos c)$

the unit vector is hence $\frac{1}{r} (r\cos a, r\cos b, r\cos c) = (\cos a, \cos b, \cos c)$ , which has a magnitude of 1.

$\implies \sqrt{\cos^2 a + \cos^2 b + \cos^2 c} = 1$

$\implies \cos^2 a + \cos^2 b + \cos^2 c = 1$

QED