Lecture02_Vectors_Review

Lecture02_Vectors_Review - 9 Properties of Vectors...

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Unformatted text preview: 9 Properties of Vectors Magnitude , length , or norm of a vector a : || a || If then: > =< 2 1 a a , a 2 2 2 1 a a + = || || a 1 || || 1 = = u with a a u j i 2 1 2 1 2 1 , , , a a a a a a + = > < + > < = > < The i , j unit vectors : i =<1,0>, j =<0,1> Example: Given a =<3,-4>, form a unit vector in the same direction as a . Answer: <0.6,-0.8> In the opposite direction of a. Answer: <-0.6,0.8> A vector that has magnitude 1 is called unit vector . A unit vector in the direction of a is : i j u 10 7.2 Vectors in 3-Space Rectangular or Cartesian Coordinate 2D-Space : Two orthogonal axes The three axes follow the Right Hand Rule : Three mutually orthogonal axes Space- 3D 11 Coordinate Plane: Each pair of coordinate axes determines a coordinate plane (xy,xz and yz). Octant :The coordinate planes divide the 3-space into 8 parts known as Octants ....
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Lecture02_Vectors_Review - 9 Properties of Vectors...

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