M23Fall02 Sample Exam 1 - Mathematics 23 Midterm Exam Answer all questions and be sure to show all work No notes books or calculators are allowed 1 a

M23Fall02 Sample Exam 1 - Mathematics 23 Midterm Exam...

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Mathematics 23 Midterm Exam, September 26, 2002Answer all questions and be sure toshow all work. No notes, books, or calculatorsare allowed.1. a. Describe in words the three dimensional region represented by the inequalityx2+y21.b. Write inequalities to describe the half-space consisting of all points to the rightof thexzplane.2. Find a unit vector that is orthogonal to bothi+jandi+k.3.Find an equation of the plane that passes through the point (1,4,2) andcontains the linex= 3t, y= 2 +t, z= 2-t.4. Consider the curve given by the parametric equationsx=t2, y=t2, z=t3.a. Find the unit tangent vector at the point (4,4,-8).b. Find parametric equations for the tangent line at (4

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