# Checking that a parametric curve is general helix

#### demonelite123

i have the curve a(t) = (3t, 2t2, 2t3) and that a'(t) = (3, 4t, 6t2). my textbook tells me to verify that the tangent lines make a constant angle with the line y = 0, z = x so basically the vector (1, 0, 1).

using the definition of the dot product $a * b = |a| |b| cos(\theta)$ i have $cos(\theta) = \frac{3 + 6t^2}{\sqrt{2}\sqrt{9 + 16t^2 + 36t^4}}$

however it doesn't look to me that this is will give a constant angle. the parameter t doesn't seem to cancel out so it wouldn't be constant in this case. have i missed something?

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#### ForMyThunder

i have the curve a(t) = (3t, 2t2, 2t3) and that a'(t) = (3, 4t, 6t2). my textbook tells me to verify that the tangent lines make a constant angle with the line y = 0, z = x so basically the vector (1, 0, 1).

using the definition of the dot product $a * b = |a| |b| cos(\theta)$ i have $cos(\theta) = \frac{3 + 6t^2}{\sqrt{2}\sqrt{9 + 16t^2 + 36t^4}}$

however it doesn't look to me that this is will give a constant angle. the parameter t doesn't seem to cancel out so it wouldn't be constant in this case. have i missed something?
Are you sure it is (3t,2t^2,2t^3) and not (3t,3t^2,2t^3)? Because it would work if it was.

#### demonelite123

i noticed that too. i'm guessing its just a typo in the book since changing it to a 3 makes it work out perfectly. thanks for your reply!

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