Exam1-Chapter10

Exam1-Chapter10 - Math 2350 Calculus III Review for Exam...

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Math 2350 Calculus III Review for Exam One 10.1 & 10.2: Vectors and Coordinate Space Know the following definitions, theorems, and formulas: equations of the coordinate planes (e.g. the xy -plane is z = 0) standard equation of a sphere displacement vector PQ  initial point, terminal point zero vector components standard basis vectors Two vectors are equivalent if they have the same magnitude and direction; equivalent vectors have the same components scalar, scalar multiple magnitude unit vector vector properties, page 526 resultant Be able to do the following: Find projections of equations and points onto the coordinate planes Find the equation of a sphere; put a sphere equation into standard form by completing the square Write inequalities to describe a given region Add or subtract two vectors algebraically or geometrically Find linear combinations of vectors (e.g. 32 uv ) Find magnitude of vectors; find a unit vector or a vector with a specified magnitude Prove properties of vectors algebraically, and demonstrate geometrically Solve a problem involving a resultant force 10.3 & 10.4 Dot Product and Cross Product Know the following definitions, theorems, and formulas: definition and properties of the dot product, page 531 Theorem 3, page 532 0 = a b if and only if a and b are orthogonal vector projection, scalar projection work done definition of cross product
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properties of the cross product, page 541 magnitude and direction of the cross product torque Be able to do the following: Find dot and cross products, algebraically and geometrically Use the dot product to find the angle between vectors or to determine if two vectors are orthogonal
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This note was uploaded on 12/08/2011 for the course MATH 20C 20C taught by Professor Boonyeap during the Fall '07 term at UCSD.

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Exam1-Chapter10 - Math 2350 Calculus III Review for Exam...

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