I have this question: Show that the tangent lines to the curve [tex]\alpha (t)= (3t,2t^2,2t^3)[/tex] make a constant angle with the line y=0 and z=x.(adsbygoogle = window.adsbygoogle || []).push({});

Now what I have done is, well obviously we have:

[tex] (1)cos(\gamma (t)) = \frac{\alpha '(t) \cdot v}{|v| |\alpha '(t)|}[/tex] 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.

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