What is Tangent vector: Definition and 55 Discussions
For a more general — but much more technical — treatment of tangent vectors, see tangent space.In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in Rn. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of germs. Formally, a tangent vector at the point
x
{\displaystyle x}
is a linear derivation of the algebra defined by the set of germs at
Homework Statement
Let bar r(t) = < -1t^(2)+2, -3e^(5t), -5sin(-4t) >
Find the unit tangent vector `bar T(t)` at the point `t=0`
The Attempt at a Solution
Attempt:
r(t) = -1t^2 + 2, -3e^5t, -5sin(-4t)
v(t) = -2t, -3e^5t, -5cos(-4t)*-4
T(t) = (-2t - 3e^(5t) -...
I see in my notes (I don't carry The Encyclopedia Britannica around with me) that George Mostow, in his artical on analytic topology, says "The set of all tangent vectors at m of a k-dimensional manifold constitutes a linear or vector space of which k is the dimension (k real)." Well ok, maybe...
Unit tangent vector in 3D - and what am I doing wrong with latex?
Question: At a given point on a curve, does the unit tangent vector given by
\frac{\vec{r}'(t)}{|\vec{r}'(t)|}
depend on the direction in which the curve is being swept out?
My initial thought on this was that the unit...
positon vectors r(t) find the unit tangent vectors T(t) for the given value of t
r(t) = (cos5t, sin5t)
T(pi/4) = ( , )
r(t) = (t^2, t^3)
T(1) = ?
r(t) = e^5t i + e^-1t j + t k
T(2) = ? i+ ? j+ ? k
now the to find it i use r'(t)/lr'(t)l
I did that, but i get...
Space Curves --> Unit Tangent Vector and Curvature
Here is the original question:
Consider the space curve r(t) = (e^t)*cos(t)i + (e^t)*sin(t)j + k. Find the unit tangent vector T(0) and the curvature of r(t) at the point (0,e^(pi/2),1).
I believe I have found the unit tangent vector...