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Material Type: Exam; Professor: Palais; Class: Calculus III; Subject: Mathematics; University: University of Utah; Term: Fall 2008;
Typology: Exams
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Calculus III, Math 2210-90, Fall 2008, Bob Palais Exam 1, Chapter 11 Vectors, Curves, and Surfaces
calculators.^ Show all your work on the exam for full credit.^ You may use graphing (or regular) The main topics covered in this exam are:
ric) and from various data (e.g. two points, point and parallel vectors)2. Vector equations of lines in 2D and 3D in various forms (e.g. parametric, symmet- and from various data (e.g. three points, point and parallel vectors)3. Vector equations of planes in 3D in various forms (e.g. parametric, point-normal)
lines or planes.4.^ Distance from a point to a line or plane.^ Distance between two non-intersecting
U · U = V · V = 1, U · V =^12 ,
and U × V =
Find the following quantities: a) (5 points) ||U + V||^2 = b) (5 points) The angle θ between U and V: c) (5 points) (V − U) · (U × V) = d) (5 points) V × (2U + 3V) =