# Find the curvature?

1. Jan 17, 2015

### Math10

1. The problem statement, all variables and given/known data
Find the curvature of r(t)=2ti+2tj+k.

2. Relevant equations
None.

3. 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?

2. Jan 17, 2015

### Staff: Mentor

Yes.
r'(t)r''(t) = 0, which you already found. What is |r'(t)|? Note that this means the magnitude or length of r'(t).

3. Jan 18, 2015

### Math10

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

4. Jan 18, 2015

### SteamKing

Staff Emeritus
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.

5. Jan 18, 2015

### haruspex

The problem is that Math10 quoted the formula using abs() instead of modulus.
It should be $k(t)=\frac{|\dot{\vec r}(t)\times \ddot {\vec r}(t)|}{|\dot{\vec r}(t)|^3}$

6. Jan 18, 2015

### Staff: Mentor

Three of us have told you that |r'(t)| does not mean "absolute value". It means "magnitude" or "length" of the vector r'(t).