Unit Tangent Vectors for Position Vectors: Finding T(t) for Given Values of t

In summary, To find the unit tangent vectors T(t) for a given value of t, the first step is to take the derivative of the position vector r(t). Then, divide the derivative by its magnitude to get the unit tangent vector T(t). However, there may be errors in the steps taken, so it is important to double check the calculations.
  • #1
weckod
13
0
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 wrong answers i don't know what I am doing wrong because all i c is that is how u find the unit tangent vectors... someone please help me and explain what u did.. thanks alot!
 
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  • #2
the derivative is the tangent vector.
then divide it by its magnitude to get unit tangent vector.
 
  • #3
I did that and the damn computer say i got the wrong answers... like the 1st one i took it derivative then i divid it by its magnitude which is squaring everything and sq rt it right that's what i did..
 
  • #4
give the answer that you have found for the first one.
 
  • #5
well i worked out the second one i got (1, 1) i really I am doing something stupid
 
  • #6
i get 2/sq rt of 13, 3/ sq rt of 13
what is wrong with your steps?
 

1. What is a unit tangent vector in Calculus 3?

A unit tangent vector is a vector that has a magnitude of 1 and is tangent to a curve at a specific point. It is used in Calculus 3 to find the direction of the curve at that point.

2. How is a unit tangent vector calculated?

To calculate a unit tangent vector, you first need to find the derivative of the curve at the given point. Then, divide the resulting vector by its magnitude to obtain a unit vector in the same direction as the tangent vector.

3. Why is the unit tangent vector important in Calculus 3?

The unit tangent vector is important in Calculus 3 because it helps determine the direction of a curve at a specific point. It is also used in calculating the curvature of a curve and in finding the unit normal vector.

4. Can a unit tangent vector be negative?

No, a unit tangent vector cannot be negative. By definition, a unit vector has a magnitude of 1, which means it cannot have a negative magnitude. However, the direction of the unit tangent vector can be positive or negative.

5. How is the unit tangent vector related to the unit normal vector?

The unit tangent vector and the unit normal vector are perpendicular to each other. This means that the dot product of these two vectors is equal to 0. In other words, the unit tangent vector and the unit normal vector are orthogonal to each other.

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