Email me in ~ this attend to if my answer is selected or comment on:Email me if my answer is selected or commented on

### tastecraftedmcd.com recommends

smallq9
The systems to the vector is below:   content_user

Given(R(t)=)and point()

The point()occursat t=-2

Find the derivative the the vector,

(R"(t)=)

(|R"(t)|=sqrt(2t)^2+(2t^2)^2+1^2)

(=sqrt4t^2+4t^4+1)

(=sqrt(2t^2+1)^2)

(=2t^2+1)

Tangent vectors:

(T(t)=fracR"(t)R"(t))

(=frac12t^2+1)

(T(-2)=frac12(-2)^2+1)

(T(-2)=frac12(-2)^2+1)

(=)

(T"(t)=)

(=)

(=)

(|T"(t)|=sqrtfrac(2-4t^2)^2+(4t)^2+(-4t)^2(2t^2+1)^4)

(=frac1(2t^2+1)^2sqrt4-16t^2+16t^4+16t^2+16t^2)

(=frac1(2t^2+1)^2sqrt16t^4+16t^2+4)

(=frac2(2t^2+1)(2t^2+1)^2)

(=frac22t^2+1)

The typical vectors.

You are watching: Find the vectors t, n, and b at the given point.

(N(t)=fracT"(t)T"(t)=frac1(2t^2+1)^2cdotfrac2t^2+12)

(=frac1(2t^2+1))

(N(-2)=frac1(2(-2)^2+1))

(=)

The binormal vector is,

(B(-2)=T(-2) imes N(-2))

(=eginvmatrixi&j&k\-frac49&frac89&frac19\-frac79&-frac49&frac49endvmatrix)

(=(frac3281+frac481)i-(-frac1681+frac781)j+(frac1681+frac5681)k)

(=)

### Relevant Questions

Find the unit tangent and also unit normal vectors T(t) and also N(t). (displaystylerleft(t ight)=)

Given the vector (r(t) = cos T, sin T, ln ( cos T) ) and point (1, 0, 0) find vectors T, N and B at the point.

Vector T is the unit tangent vector, for this reason the derivative r(t) is needed.

Vector N is the common unit vector, and also the equation because that it offers the derivative of T(t). ()

The B vector is the binormal vector, i m sorry is a crossproduct the T and N.

Find (displaystyleleft(t ight),Nleft(t ight),a_T,quad extandquada_N) at the provided time t for the aircraft curver r(t). (displaystylerleft(t ight)=t^2i+2tj,t=1)

Let W it is in the collection of all vectors the the kind shown, whereby a, b, and also c represent arbitrary actual numbers. In every case, either find a set S of vectors the spans W or give an instance to present that W is not a vector space.

See more: Top 10 Tips To Speed Up Chrome Browser Up To 5 Times Fast Tab/Window Close

<eginbmatrix4a+3b \ 0 \ a+b+c \ c-2a endbmatrix>

Find the major unit typical vector come the curve at the stated value of the parameter(displaystylerleft(t ight)=ti+frac6tj,t=3)

Find the principal unit common vector to the curve at the specified value of the parameter(r(t)=ti+frac6tj , t=3)

Vector overcome ProductLet vectors A=(1,0,-3), B =(-2,5,1), and also C =(3,1,1).Calculate the following, expressing her answers together ordered triples (three comma-separated numbers).(C) (displaystyleleft(2overlineB ight)left(3overlineC ight))(D) (displaystyleleft(overlineB ight)left(overlineC ight))(E) (displaystyleover ightarrowAleft(over ightarrowB imesover ightarrowC ight))(F)If (displaystyleoverlinev_1 ext and overlinev_2) space perpendicular, (displaystyleoverlinev_1 imesoverlinev_2 ight)(G) If (displaystyleoverlinev_1 ext and also overlinev_2) room parallel, (displaystyleoverlinev_1 imesoverlinev_2 ight) 