# Baby Do-Carmo's question.

1. Jul 15, 2011

### MathematicalPhysicist

I have this question: Show that the tangent lines to the curve $$\alpha (t)= (3t,2t^2,2t^3)$$ make a constant angle with the line y=0 and z=x.

Now what I have done is, well obviously we have:
$$(1)cos(\gamma (t)) = \frac{\alpha '(t) \cdot v}{|v| |\alpha '(t)|}$$ So what I have done is to take the derivative of the RHS in (1) wrt t, where v=(x,0,x).
My reasoning is that if the derivative is zero then the angle is constant.

My problem is that I don't get zero, where did I get it wrong?

Thanks.

2. Jul 15, 2011

### Fredrik

Staff Emeritus
If we're supposed to show that the tangent vectors of $\alpha$ make a constant angle with the tangent vectors of that line, then it seems to me that what we have to show is that $$\frac{d}{dt}\big(\alpha'(t)\cdot(1,0,1)\big)=0$$ for all t. This is obviously not true, so I'm wondering if he might have meant something else. But I don't see how he could have meant something that makes the claim true.

3. Jul 15, 2011

### MathematicalPhysicist

Well, I guess you also have a copy of the book right?

Anyway, here's a scan for the others.

question 1.

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4. Jul 15, 2011

### Fredrik

Staff Emeritus
I don't have a copy of the book, but I don't mind downloading a pdf for purposes like this. I have skimmed the first few pages now. I didn't see any hints that he might have meant something different.

5. Jul 15, 2011

### MathematicalPhysicist

For me 'copy' doesn't necessarily mean hard copy.

Thanks, anyway.