Q : the non−zero vector a^→ = (a_1 , a_( 2) , a_( 3) ) with the coordinate axes makes the angles , α , β and γ . prove that the following equality. cos^( 2) (α ) +cos^( 2) (β )+ cos^( 2) ( γ )= 1


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Question Number 188881 by mnjuly1970 last updated on 08/Mar/23

$Q : the non - zero vector \vec{a} = (a_{1}, a_{2}, a_{3}) with$ $the coordinate axes makes the$ $angles, α, β and γ . prove$ $that the following equality .$ $\cos^{2} (α) + \cos^{2} (β) + \cos^{2} (γ) = 1$
	Answered by mr W last updated on 08/Mar/23

	$d = \sqrt{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}$ $\Rightarrow \cos α = \frac{a_{1}}{d}$ $\Rightarrow \cos β = \frac{a_{2}}{d}$ $\Rightarrow \cos γ = \frac{a_{3}}{d}$ $\cos^{2} α + \cos^{2} β + \cos^{2} γ = \frac{a_{1}^{2} + a_{2}^{2} + a_{3}^{2}}{d^{2}} = 1$
	Commented by mnjuly1970 last updated on 08/Mar/23

	$t h a n k s a l o t s i r W$
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