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T02.1 Vectors

T02.1 Vectors - Vectors T02.1 Vector:A A A Magnitude...

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Vectors T02.1
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Vector: A Magnitude A = | A | = length of A Direction Obeys parallelogram law of addition ± A ± A ± A ± B + ± ± A B G A ± A
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Vector Resolution x z y F F x F z F y M z M x M y M = + + = + + = + + ± ± ± ± ± ± ± 2 2 2 x y z x y z x y z F F F F F i F j F k F F F F F
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Vector Addition Trigonometry (2D) Parallelogram law of addition Law of sines Law of cosines Vector resolution (2D & 3D) ( ) ( ) ( ) ( ) ( ) + = + + + + + = + + + + + + ± ± ± ± ± ± ± ± ± ± ± ± ± 1 2 1 1 1 2 2 2 1 2 1 1 2 2 1 2 x y z x y z x x y y z z A A A i A j A k A i A j A k A A i A A j A A A A k
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Example Find: Compute the resultant, F R = F 1 + F 2 . x y z F 1 = 45 N F 2 = 60 N 35 o 40 o 30 o
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Unit Vector, u “Derivation” Definition = = ± ± ± A A A A Au A α β γ = = = + + = + + ± ± ± ± ± ± ± ± ± ± : (cos ) (cos ( ) : ) cos y x z A A A A A A A u i j k A A A A i j u A k x z y A A x A z A y
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Position Vectors, r P & r AB x y z P (x,y,z) O x y z B (x B ,y B ,z B ) O A (x A ,y A ,z A )
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Example Given: Speed of arrow is 50 ft/s Find: Assuming that the archer is a good shot and the effect of
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