4.6p_Vcontnud

# 4.6p_Vcontnud - ENGR 211 Lecture 4 ENGR 211 Lecture 4 ENGR...

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ENGR 211 Lecture 4 Fall 2007 Civil Engineering ENGR 211 Lecture 4 ENGR 211 Lecture 4 ENGR 211 Geom-Trig PreTest 0 2 4 6 8 10 12 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 Score Civil Engineering Another way to give Another way to give direction: unit vector direction: unit vector V e V

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ENGR 211 Lecture 4 Fall 2007 Civil Engineering Unit Vector: Unit Vector: • Direction of Vector (unit vector): • Magnitude of the vector: 2 22 y x z V c c c e ⎛⎞ ++ ⎜⎟ ⎝⎠ = VVV 222 z zy x z V CCC C C C e =++ xy ij k =i j k Civil Engineering unit vector unit vector V e V (cos ) (cos ) (cos ) xyz V e θθθ k
ENGR 211 Lecture 4 Fall 2007 Civil Engineering 3-D Cartesian Coordinates D Cartesian Coordinates x y z i j k (x 1 ,y 1 ,z 1 ) (x 2 ,y 2 ,z 2 ) If the magnitudes come from two points, then it looks like: 21 () ( ) x xy yz z =− +− Vij k Civil Engineering Write Write F in Cartesian form in Cartesian form | F | = 8 kN

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ENGR 211 Lecture 4 Fall 2007 Civil Engineering Dot Product Dot Product • Definition: • Properties: – It’s a scalar – Commutative – Associative
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4.6p_Vcontnud - ENGR 211 Lecture 4 ENGR 211 Lecture 4 ENGR...

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