MAT-2130 Midterm: MATH 2130 App State Fall2012 Test2 answer key
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/20 points) lines (a) let 1 be the line parametrized by r1(t) = h1 + t, 2 2t, ti and 2 be the line parametrized by r2(t) = h3 2t, 4t, 1 + 2ti. Determine if 1 and 2 are the same, parallel, intersecting, or skew. (b) parametrize the line segment through p = (1, 2, 1) and q = (3, 2, 1). T ?? (c) find a parametrization for the line tangent to r(t) = ht, t2, t3i at t = 1. /14 points) find a (scalar) equation for the plane which contains the line r(t) = h1, 2, 1i + h 1, 0, 2it and the point p = ( 3, 2, 1). /16 points) let r(t) = he t, t, sin(t)i where t 6 . (a) set up an integral which computes the arc length of the curve parametrized by r(t). Do not attempt to evaluate this integral. (b) find the curvature of r(t).
