Need help with this vector problem -- Thank you

In summary: Keep going!In summary, the problem involves finding the equations of two tangent lines, L1 and L2, to the vector function r(t) at points t=a and t=b, respectively. The steps to solve this problem include finding the tangent vector T(t) and using it to find the equations of L1 and L2. It is also important to check for any points of intersection between the two lines.
  • #1
uchuu-man chi
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Homework Statement


Let L1 be the tangent line to r(t) at the point t = a and let L2 be the tangent line where t = b. Find the equation of the lines L1. Find the equation of the lines L1 and L2 and find the points of intersection.

r(t) = <f(t), g(t), h(t)>

*bolded letters are vectors

Homework Equations

The Attempt at a Solution


I just wanted to tell you guys my thought process and would you correct me wherever I am wrong. The question has more to it, but the computation would be menial. I'm just having trouble with what vectors to use and all that stuff.

Steps I would take:
-r(a) would give me a point on L1 and r(b) would give me a point on L2.
-find T(t)
-find T(a) and T(b)
-for L1, the equation of line would be (f(a), g(a), h(a)) + T(a)t
-same step for L2 as L1
-find if there is an intersection by setting the parameters of x,y, and z of the lines equal

Am I using the correct vector, T(t), for the second step?
 
Last edited:
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  • #2
Did you forget to tell us what T is ?
And: do you always expect to find an intersection ?
 
  • #3
BvU said:
Did you forget to tell us what T is ?
And: do you always expect to find an intersection ?

OOps sorry

the T(t) would be $$\frac {\vec r '(t)} {||\vec r '(t)||}$$
And no I wouldn't expect to always find an intersection. The lines could be parallel or skew
 
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  • #4
uchuu-man chi said:
The question has more to it
In that case: so far, so good :smile: !
 
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Related to Need help with this vector problem -- Thank you

1. What is the vector problem in question?

The vector problem in question is a mathematical problem that involves the use of vectors, which are quantities that have both magnitude and direction. The problem may require finding the magnitude and direction of a given vector, or performing mathematical operations on multiple vectors.

2. Why do I need help with this vector problem?

Vectors can be complex and require a thorough understanding of mathematical concepts such as trigonometry and vector operations. Additionally, different types of vector problems may have unique approaches and strategies for solving them. Seeking help can provide clarity and guidance in tackling the problem.

3. How can I solve this vector problem?

The specific method for solving a vector problem will depend on the given information and the type of problem. However, some general steps for solving vector problems include identifying the given and required quantities, drawing a vector diagram, and using mathematical equations and operations to find the solution.

4. What are some common mistakes when solving vector problems?

One common mistake when solving vector problems is forgetting to take into account the direction of the vectors. Another mistake is using the wrong mathematical operations or equations for the given problem. It is also important to double-check calculations and units to ensure accuracy.

5. Can you provide an example of a vector problem?

Sure! An example of a vector problem could be finding the resultant velocity of a boat that travels 20 km/h north for 2 hours and then 30 km/h east for 1 hour. To solve this problem, you would need to use vector addition to find the magnitude and direction of the resultant velocity vector.

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