Consider the following curves: r₁(t) = (sint, sint, √2 cost), r2(t)=(√2 cost, √2 sint,0), t = [0, 2π] (a) Find the points where the curves intersect (b) Find the angle between these curves at the points of intersection (c) Show that the curves are circles on a sphere. Answer: (a) The curves intersect at (1,1,0) and (-1,-1,0). (b) the curves are orthogonal at these points.
Consider the following curves: r₁(t) = (sint, sint, √2 cost), r2(t)=(√2 cost, √2 sint,0), t = [0, 2π] (a) Find the points where the curves intersect (b) Find the angle between these curves at the points of intersection (c) Show that the curves are circles on a sphere. Answer: (a) The curves intersect at (1,1,0) and (-1,-1,0). (b) the curves are orthogonal at these points.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 61E
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