# 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