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 = ++ =++ = ±± ± ± ± 222 xyz FF F F Fi Fj Fk 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) ( ) ( ) () += + + + + + =+ ++ + + + ±± ± ± ± ± ± ± ± 12 1 1 1 2 2 2 1 21 2 xyz xx yy zz A A A iA j A k A j A k AA i j 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 AA u A α βγ = + + =++ ± ±± ± ± ± ± ± ± ± : (cos ) (cos ( ) : )c o s y xz A A A A A ui j k A A ij 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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This note was uploaded on 12/19/2010 for the course EGR 75 taught by Professor Virgin during the Fall '08 term at Duke.

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

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