salas10_ppt_ch13_checked - Chapter 13 Vectors In Three-Dimensional Space Section 13.1 Rectangular Space Coordinates a Right-Hand Rule b Rectangular(or

salas10_ppt_ch13_checked - Chapter 13 Vectors In...

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Salas, Hille, Main Menu Chapter 13: Vectors In Three-Dimensional Space Section 13.1 Rectangular Space Coordinates a. Right-Hand Rule b. Rectangular (or Cartesian) Coordinates c. Distance Formula d. Equation of a Sphere e. Symmetry f. Theorem 12.1.4 g. Midpoint Formula Section 13.2 Vectors In Three-Dimensional Space a. Vector Components b. Geometric Interpretation of Vectors c. Visualizing a + b d. Norm e. Scalar Multiples f. Summation of Vectors g. Parallel Vectors h. Illustration of Parallel Vectors i. Unit Vectors Section 13.3 The Dot Product a. Definition b. Properties of the Dot Product c. More Properties d. Geometric Interpretation of the Dot Product e. Law of Cosines f. Perpendicular Vectors g. Projections and Components h. Direction Angles, Direction Cosines i. Schwarz’s Inequality Section 13.4 The Cross Product a. Definition b. Right-Handed Triples c. Properties of Right-Handed Triples d. Properties of Cross Product e. Scalar Triple Product f. Components of a x b g. Theorems Section 13.5 Lines a. Vector Parameterizations b. Scalar Parametric Equations, Symmetric Form, Intersecting Lines c. Distance from a Point to a Line Section 13.6 Planes a. Scalar Equation b. Vector Equation c. Unit Normals, Parallel and Intersecting Planes d. Three Noncollinear Points e. Distance from a Point to a Plane
Salas, Hille, Main Menu Rectangular Space Coordinates Right-hand rule : if the fingers of the right hand are curled from the positive x - axis toward the positive y -axis (the short route), the thumb points along the positive z -axis. The point on the x -axis with x -coordinate x 0 is given space coordinates ( x 0 , 0 , 0); the point on the y -axis with y -coordinate y 0 is given space coordinates (0 , y 0 , 0); the point on the z -axis with z -coordinate z 0 is given space coordinates (0 , 0 , z 0 ).
Salas, Hille, Main Menu Rectangular Space Coordinates There are now three coordinate planes; the xy -plane, the xz -plane, the yz -plane. A point P in three-dimensional space is assigned coordinates ( x 0 , y 0 , z 0 ) provided that (1) the plane through P which is parallel to the yz -plane intersects the x -axis at ( x 0 , 0 , 0), (2) the plane through P which is parallel to the xz -plane intersects the y -axis at (0 , y 0 , 0), (3) the plane through P which is parallel to the xy -plane intersects the z

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