Practice 1

# Practice 1 - Math E-21a Midterm Exam 1 Topics Fall 2009 1...

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Math E-21a – Midterm Exam 1 Topics – Fall 2009 1. Given vectors in R 2 or R 3 , do addition, scalar multiplication, dot and cross products, scalar and vector projection. 2. Manipulate vector expressions symbolically (distributive law, triple product, A ( B C ), etc.). 3. Express lengths, angles, areas of triangles and parallelograms, and volumes of parallelepipeds and tetrahedra in terms of vectors. Identify and construct orthogonal (perpendicular) vectors. 4. Given sufficient data, describe a line or plane either parametrically or in terms of one or more equations involving x , y , and z . 5. Calculate the intersection (if any) of specified lines and planes. Resolve a vector into components parallel and perpendicular to a specified vector, line, or plane. 6. Calculate the distance from a point to a specified line or plane, or between two nonintersecting lines in R 3 . 7. For motion in R 2 or R 3 specified parametrically in terms of time, calculate and sketch position, velocity, and acceleration vectors, and find an expression for the tangent line to the path at a specified point and for the unit tangent vector. 8. Write one or more parameterized expressions for a specified path in R 2 or R 3 . 9. Develop an expression for the length of a parameterized path as an integral. 10. Sketch a graph of a parameterized path, and eliminate the parameter (if possible) to find an equation or equations in terms of x , y , (and z ) for the path.

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## This note was uploaded on 02/10/2011 for the course MATH E-21a taught by Professor - during the Fall '09 term at Harvard.

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Practice 1 - Math E-21a Midterm Exam 1 Topics Fall 2009 1...

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