handout 12-1 and 12-2

handout 12-1 and 12-2 - Math 200, Spring 2010 Handout 1...

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Math 200, Spring 2010 Handout 1 Section 12-1 Vectors in the Plane Section 12-2 Vectors in Three Dimensions Three-Dimensional Rectangular Coordinate System Coordinate axes : The x -axis, y -axis, z -axis are perpendicular to each other. Right-hand rule : The fingers of the right hand curl from the positive x -axis to the positive y -axis. The thumb points in the positive z -direction. Coordinates of point P are the ordered triple ( ) , , a b c of real numbers. Coordinate planes in 3 are defined by setting one of the coordinates to zero. The xy -plane consists of the points ( ) , ,0 a b and is defined by equation 0 z = . The yz -plane consists of the points ( ) 0, , b c and is defined by equation 0 x = . The xz -plane consists of the points ( ) ,0, a c and is defined by equation 0 y = . The coordinate planes divide 3 into eight Octants. The set of points ( ) , , a b c with , , 0 a b c > is called the First Octant . In two-dimensional geometry, the graph of an equation involving x and y is a curve in 2 . In three-dimensional geometry, the graph of an equation involving x, y, and z is a surface in 3 . 1. Sketch the points ( ) 2,3,5 and ( ) 1, 3,2 − − on 2. What does the equation 4 x = represent in 2 ? a single set of coordinate axes. What does the equation 4 x = represent in 3 ? Illustrate with a sketch.
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Projections of P on a Coordinate Plane. The point ( ) , , P a b c determines a rectangular box. If we drop a perpendicular from P to the xy -plane, we get a point Q with coordinates ( ) , ,0 a b called the projection of P on the xy -plane. Similarly, ( ) 0, , R b c and ( ) ,0, S a c are the projections of P on the yz -plane and xz -plane, respectively. 3.
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This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

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handout 12-1 and 12-2 - Math 200, Spring 2010 Handout 1...

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