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^{2}, 2t

^{3}) and that a'(t) = (3, 4t, 6t

^{2}). 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 [itex] a * b = |a| |b| cos(\theta) [/itex] i have [itex] cos(\theta) = \frac{3 + 6t^2}{\sqrt{2}\sqrt{9 + 16t^2 + 36t^4}} [/itex]

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?