Something about tangent vector

[maki1314]

hey there, i got stuck on an question here:
Parameterise the following paths, in the dirction stated, and hence find a tagent vector(in the same dirction) to each point on the paths.
(a)The upper part of the circled centred at (0,0) containing the points (-2,0) and (2,0) going anticlockwise.
(b) the circle centred at (1,2,5) of radius three in the plane z=5 going clockwise (looking down the z axis)

lol,really need help on these two questions. Thx everyone

 

[rs1n]

hey there, i got stuck on an question here:
Parameterise the following paths, in the dirction stated, and hence find a tagent vector(in the same dirction) to each point on the paths.
(a)The upper part of the circled centred at (0,0) containing the points (-2,0) and (2,0) going anticlockwise.
(b) the circle centred at (1,2,5) of radius three in the plane z=5 going clockwise (looking down the z axis)

lol,really need help on these two questions. Thx everyone

Can you tell us what you have attempted? In particular, do you have a clear understanding of what "tangent vector" means?

 

[maki1314]

Can you tell us what you have attempted? In particular, do you have a clear understanding of what "tangent vector" means?

honestly, i attempt another 3 similar questions but really have no idea on that one. all my understanding is that tangent vec. is the trace of a curve at given points...something like that hum? not sure if my understanding is correct...lol

 

[rs1n]

honestly, i attempt another 3 similar questions but really have no idea on that one. all my understanding is that tangent vec. is the trace of a curve at given points...something like that hum? not sure if my understanding is correct...lol

A tangent vector is essentially a vector that is tangent to the graph of your curve. Surely you know what "tangent" and "vector" mean. If you think of your curve as a position function (written in the form of a vector; see below), the tangent vector is equivalent to the velocity vector. The problem requires that you come up with a set of parametric equations x(t) and y(t) that would describe the position of a point on the specified curves. Then, using this position function, determine the tangent vector.

If $\vec{r}(t)$ is the position vector, then

$$\vec{r}(t) = x(t) \vec{\mathbf{i}} + y(t) \vec{\mathbf{j}}$$