The problem involves finding the curvature of the vector function r(t) = 2ti + 2tj + k. The context is centered around vector calculus and the specific application of curvature formulas.
The discussion is ongoing, with participants providing guidance on the interpretation of vector magnitudes and the correct application of curvature formulas. There is a focus on understanding the notation used in the problem.
Some participants note confusion regarding the notation used for vector magnitudes, specifically the use of "abs()" versus "modulus". There is an emphasis on ensuring clarity in mathematical terminology.
Yes.Math10 said:Homework Statement
Find the curvature of r(t)=2ti+2tj+k.
Homework Equations
None.
The Attempt at a Solution
The answer is 0 in the book.
I know the formula for curvature is k(t)=abs(r'(t)xr"(t))/abs(r'(t))^3. I know that r'(t)=2i+2j and r"(t)=0, so r'(t)xr"(t)=0?
r'(t)r''(t) = 0, which you already found. What is |r'(t)|? Note that this means the magnitude or length of r'(t).Math10 said:How to find r'(t)xr"(t) and r'(t)^3?
Math10 said:So how do I find abs(r'(t))? That's where I got stuck.
The problem is that Math10 quoted the formula using abs() instead of modulus.SteamKing said:The notation |r'(t)| does not mean the absolute value of r'(t), it means to find the magnitude of the vector r'(t). Think Pythagoras.
Three of us have told you that |r'(t)| does not mean "absolute value". It means "magnitude" or "length" of the vector r'(t).Math10 said:So how do I find abs(r'(t))? That's where I got stuck.