Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating...

Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic.

a) Find the osculating circle for this twisted cubic at t = 0.

b) Try to do the same for the ordinary cubic parabola ¯r(t) = <t, 0, t^3 >. Explain why did you fail to do that.

Expert Solution

milcah answered 2 years ago

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the point corresponding to ? = 1. (b) Find the equation of the osculating plane at the point corresponding to ? = 1. (c) Find the equation of the normal plane at the point corresponding to ? = 1

Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of...

Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of R^(2x2) be the standard matrix of T. In a) and b) below, by rotation we mean "rotation of R^2 by some angle and the origin". By reflection, we mean "reflection of R^2 over some line through the origin". a) Show that T is either a rotation or a reflection. b) Show that every rotation is a composition of 2 reflections, and thus that T...

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Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating...

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