Week1_2 - ENGR210, Fall 2011 EXAMPLE 2.5 1 ENGR210, Fall...

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ENGR210, Fall 2011 1 EXAMPLE 2.5
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ENGR210, Fall 2011 2 SOLUTION
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ENGR210, Fall 2011 3 Therefore Note that an arrow is shown to indicate the direction for a vector component. If a coordinate system is clearly depicted in your answer, which should be, then you don’t have to re-write your answers using arrows. The Cartesian notation is
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ENGR210, Fall 2011 4
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ENGR210, Fall 2011 5
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ENGR210, Fall 2011 6 2.5 Cartesian vectors (3D) Cartesian expression Magnitude
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ENGR210, Fall 2011 7 “Direction of a (3D) Cartesian vector” The coordinate direction angles ( α , β and γ ) define the direction of A . α , β and γ are between 0 and 180°.
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ENGR210, Fall 2011 8 The angles can be determined as using the direction cosines , where
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ENGR210, Fall 2011 9 A unit vector of A , u A , can be expressed as (The unit vector expression above is very important!) Using the direction cosines, the equation above is
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10 Because the magnitude of a unit vector is 1, an important relation between the direction cosines is
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Week1_2 - ENGR210, Fall 2011 EXAMPLE 2.5 1 ENGR210, Fall...

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