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  • Publicado : 25 de enero de 2012
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S= (T^2+4)i-cos2tj+sen2tk
(dS(t))/dt=2ti+2sen2tj+2cos2tk
|(dS(t))/(d(t))|=√((〖2t)〗^2+(〖2sen2t)〗^2+(〖2cos2t)〗^2 )
|(dS(t))/(d(t))|=√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)
T (t)=((dS(t))/dt)/|(dS(t))/(d(t))| =(2ti+2sen2tj+2cos2tk)/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)
T (t) = 2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t) i+2sen2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)j+2cos2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t) k

Vector unitario tangente
dT(t)/dt=(√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)-8t^2)/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2) i+2cos2t(√(4t^2+4〖sen〗^22t+4〖cos〗^2 2t)-8t^2 )sen2t/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2) j
-2sen2t(√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)-8t^2 )/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2) k
|(dT(t))/(d(t))|=√(((√(4t^2+4〖sen〗^22t+4〖cos〗^2 2t)-8t^2)/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2) )^2+(2cos2t(√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)-8t^2 )sen2t/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2))^2-((2sen2t((√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)-8t^2 ))/(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)^(3⁄2) )^2 )
N(t)= (dT(t)/dt)/|(dT(t))/(d(t))| i+(dT(t)/dt)/|(dT(t))/(d(t))| j-(dT(t)/dt)/|(dT(t))/(d(t))| k
Vectorunitario normal
B (t)= T(t)xN(t)
=|■(i&j&k@ 2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)&2sen2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t)&2cos2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^22t)@(dT(t)/dt)/|(dT(t))/(d(t))| &(dT(t)/dt)/|(dT(t))/(d(t))| &-(dT(t)/dt)/|(dT(t))/(d(t))| )|

Vector unitario binormal
B(t)=[(2sen2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t))(-(dT(t)/dt)/|dT(t)/d(t) |k)-(2cos2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t))((dT(t)/dt)/|dT(t)/d(t) | j)]i+[(2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t))(-(dT(t)/dt)/|dT(t)/d(t) | k)-(2cos2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^22t))((dT(t)/dt)/|dT(t)/d(t) | i)]j+[(2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t))((dT(t)/dt)/|dT(t)/d(t) | j)-(2sen2t/√(4t^2+4〖sen〗^2 2t+4〖cos〗^2 2t))((dT(t)/dt)/|dT(t)/d(t) |...
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