'''접벡터''' or '''접선벡터'''

$\vec{r}(t)$ 가 parametric smooth curve일 때, // [[매끄러움,smoothness]] [[곡선,curve]] [[매끄러운곡선,smooth_curve]]
'''tangent vector'''는:
 $\vec{r}{}'(t)$
'''unit tangent vector'''는: ([[단위접벡터,unit_tangent_vector]])
 $\vec{T}(t)=\frac{\vec{r}{}'(t)}{|\vec{r}{}'(t)|}$

Compare: (tangent 시리즈)
[[접선,tangent_line]]과 유사? (curr. goto there)
[[접평면,tangent_plane]]?

see also [[MIT_Multivariable_Calculus#s-6]]

Sub: [[단위접벡터,unit_tangent_vector]]

mathworld는 [[반지름벡터,radius_vector]]를 먼저 정의 
 -> 반지름벡터는 [[위치벡터,position_vector]]와 동의어

rel, mklink
[[곡선,curve]] esp [[공간곡선,space_curve]](curr see [[벡터함수,vector_function#s-7]])

= Bazett =
곡선 위의 한 점의 [[위치벡터,position_vector]] $\vec{r}(t)$ 가정.
$\frac{d\vec{r}}{dt}$ 를 어떻게 구할 것인가? 우선
 $\frac{\Delta\vec{r}}{\Delta t}=\frac{\vec{r}(t+\Delta t)-\vec{r}(t)}{\Delta t}$
여기서 $\Delta t\to 0$ 극한을 생각하면
 $\frac{d\vec{r}}{dt}=\lim_{\Delta t\to 0}\frac{\vec{r}(t+\Delta t)-\vec{r}(t)}{\Delta t}$
그리고 $\vec{r}(t)=f(t)i+g(t)j+h(t)k$ 라면
 $\vec{r}(t+\Delta t)-\vec{r}(t)$
 $=[f(t+\Delta t)i+g(t+\Delta t)j+h(t+\Delta t)k]-[f(t)i+g(t)j+h(t)k]$
 $=[f(t+\Delta t)-f(t)]i+[g(t+\Delta t)-g(t)]j+[h(t+\Delta t)-h(t)]k$
따라서 구하고자 하는 식은
 $\lim_{\Delta t\to 0}\frac{\vec{r}(t+\Delta t)-\vec{r}(t)}{\Delta t}$
 $=\lim_{\Delta t\to 0}\left(\frac{f(t+\Delta t)-f(t)}{\Delta t}\right)i+\lim_{\Delta t\to 0}(...)j+\lim_{\Delta t\to 0}(...)k$
 $=\frac{df}{dt}i+\frac{dg}{dt}j+\frac{dh}{dt}k$

Leibniz 표기법:
 $\frac{d\vec{r}}{dt}=\frac{df}{dt}\hat{\rm i}+\frac{dg}{dt}\hat{\rm j}+\frac{dh}{dt}\hat{\rm k}$
Lagrange 표기법:
 $\vec{r}{}'(t)=f'(t)\hat{\rm i}+g'(t)\hat{\rm j}+h'(t)\hat{\rm k}$

(https://youtu.be/40r56pX4mqA 3:30)

----
MKLINK
[[법벡터,normal_vector]] or [[법선벡터,normal_vector]](작성중)

할벡터? 할선벡터? [[secant_vector]]
{
'''secant vector''':
 $\vec{r}(t+h)-\vec{r}(t)$
그리고 이것도? (크기는 무관?)
 $\frac{\vec{r}(t+h)-\vec{r}(t)}{h}$

tangent vector: ([[접벡터,tangent_vector]])
 $\lim_{h\to 0} \frac{\vec{r}(t+h)-\vec{r}(t)}{h} = \vec{r}'(t)$

unit tangent vector: ([[단위접벡터,unit_tangent_vector]])
 $\frac{\vec{r}{}'(t)}{\left|\vec{r}{}'(t)\right|}=\vec{T}(t)$

(Stewart)

}

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[[https://terms.naver.com/entry.naver?docId=4125430&cid=60207&categoryId=60207 수학백과: 접벡터]]
https://mathworld.wolfram.com/TangentVector.html

Up: [[탄젠트,tangent]] [[벡터,vector]]