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

AI Thread Summary
The discussion focuses on solving vector calculus problems involving the curves r1(t) and r2(t). The user seeks assistance in determining the angle of intersection after identifying the point where the curves meet. They mention the formula |n||m| cos(a) = n.m, but express difficulty in finding the unit tangent vectors n and m at the intersection point. The known point of intersection is (3, -2, 25), which is crucial for substituting values for t and s. The thread emphasizes the need for guidance on calculating the unit tangent vectors to proceed with finding the angle of intersection.
Electro
Messages
48
Reaction score
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:
Physics news on Phys.org
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.
 
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).
 
Thread 'Struggling to make relation between elastic force and height'
Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Back
Top