Proving Constant Angle of Tangent Lines to a Curve with y=0 and z=x

[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.

 

[Fredrik]

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.

 

[MathematicalPhysicist]

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

Anyway, here's a scan for the others.

question 1.

 

[Fredrik]

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.

 

[MathematicalPhysicist]

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

Thanks, anyway.