Matematika, prosím o výpočet
Odpovědi
Diskuze
A(2,0,5)
B(3,-1,3)
C(4,-2,0)
D(5,2,-1)
E(0,0,8)
F(6,2,-1)
AB=B-A=(3,-1,3)-(2,0,5)=(1,-1,-2)
AC=C-A=(4,-2,0)-(2,0,5)=(2,-2,-5)
DE=E-D=(0,0,8)-(5,2,-1)=(-5,-2,9)
DF=F-D=(6,2,-1)-(5,2,-1)=(1,0,0)
AB×AC=(1,-1,-2)×(2,-2,-5)=(1,1,0)=u
DE×DF=(-5,-2,9)×(1,0,0)=(0,9,2)=v
cos(φ) = u*v / |u|*|v|
u*v=(1,1,0)*(0,9,2)=0+9+0=9
|u|=|(1,1,0)| = √(1*1+1*1+0*0) = √2
|v|=|(0,9,2)| = √(0*0+9*9+2*2) = √(81+4)=√85
|u|*|v| = √2 * √85 = √170
cos(φ) = 9/√170
φ = (9/170i@)io=46,348634066968323596277006166058°
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plane ((2,0,5),(3,-1,3),(4,-2,0)) , plane ((5,2,-1),(0,0,8),(6,2,-1))
https://www.wolframalpha.com/input/?i=plane+((2,0,5),(3,-1,3),(4,-2,0))+,+plane+((5,2,-1),(0,0,8),(6,2,-1))
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vector(1,1,0) , vector(0,9,2)
https://www.wolframalpha.com/input/?i=vector(1,1,0)+,+vector(0,9,2)