Solving Vector Calculus Problems in r1(t) and r2(t)

In summary, the conversation is about finding the point of intersection and angle of intersection between two curves in vector calculus. The first part is easy, but there are difficulties with the second part due to not having values for the unit tangent vectors. The formula |n||m| cos(a)=n.m is suggested to be used, but it requires the unit tangent vectors which are in terms of t. The question remains on what to substitute for t to get the value, given the known point of intersection (3,-2,25).
  • #1
Electro
48
0
Vector Calculus

Greetings everyone,

I have a problem: "Consider the curves r1(t)=(t, 1-t, 16+t^2) and
r2(t)=(8-s,s-7, s^2)
a) At what point do they meet?
b) Find their angle of intersection

The first part is easy, but I'm encountering some problems with b). To find the angle we need to apply the formula |n||m| cos(a)=n.m
The point is that we don't have the values of n and m. I tried to subsitute values for t and s (we also know the point of intersection) but still couldn't get it.
Someone can help?
Thanks
 
Last edited:
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  • #2
Apply that formula |n||m| cos(a)=n.m where n and m are the unit tangent vectors of r1 & r2 at the point of intersection.
 
  • #3
If we get the Unit Tangent Vectors then they are in terms of t. What do we substitute for t to get the value? The point we have is (3,-2,25) ->(x,y,z).
 

FAQ: Solving Vector Calculus Problems in r1(t) and r2(t)

What is vector calculus?

Vector calculus is a branch of mathematics that deals with vector fields and scalar fields, and their derivatives and integrals. It is used to study and analyze physical phenomena in fields such as physics, engineering, and economics.

What are r1(t) and r2(t) in vector calculus?

r1(t) and r2(t) are position vectors that represent the position of an object in a three-dimensional space at different points in time. They can also be considered as parametric equations that describe the movement of an object.

How do I solve vector calculus problems using r1(t) and r2(t)?

To solve vector calculus problems using r1(t) and r2(t), you will need to use various operations such as vector addition, subtraction, dot product, and cross product. You will also need to take derivatives and integrals of these vectors to find velocity and acceleration.

What are some common applications of solving vector calculus problems in r1(t) and r2(t)?

Vector calculus is used in many fields, including physics, engineering, computer graphics, and economics. Some common applications include calculating the trajectory of a projectile, analyzing the motion of objects in a fluid, and optimizing routes for vehicles or airplanes.

Are there any useful tools or resources for solving vector calculus problems in r1(t) and r2(t)?

Yes, there are many tools and resources available for solving vector calculus problems. Some useful tools include vector calculus calculators, software programs such as MATLAB or WolframAlpha, and online tutorials and practice problems. It is also helpful to have a strong understanding of basic calculus concepts and equations.

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