# Find the curvature?

## Homework Statement

Find the curvature of r(t)=2ti+2tj+k.

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? How to find r'(t)xr"(t) and r'(t)^3?

Mark44
Mentor

## Homework Statement

Find the curvature of r(t)=2ti+2tj+k.

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?
Yes.
Math10 said:
How to find r'(t)xr"(t) and r'(t)^3?
r'(t)r''(t) = 0, which you already found. What is |r'(t)|? Note that this means the magnitude or length of r'(t).

So how do I find abs(r'(t))? That's where I got stuck.

SteamKing
Staff Emeritus
Homework Helper
So how do I find abs(r'(t))? That's where I got stuck.
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.

haruspex
Homework Helper
Gold Member
2020 Award
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.
The problem is that Math10 quoted the formula using abs() instead of modulus.
It should be ##k(t)=\frac{|\dot{\vec r}(t)\times \ddot {\vec r}(t)|}{|\dot{\vec r}(t)|^3}##

Mark44
Mentor
So how do I find abs(r'(t))? That's where I got stuck.
Three of us have told you that |r'(t)| does not mean "absolute value". It means "magnitude" or "length" of the vector r'(t).