lecture02 - by number b a c Triangle inequality:...

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x y a x a y 2 - Dimensional Vectors (2D)    , , a a j a i a a a a a y x y x a a sin cos a a a a y x x y y x a a a a a tan 2 2 a a a a j i a a , a a ,a a y x y x vector of direction in the r unit vecto - directions y and in x, ors unit vect - , vector of vectors component vector of scalars) ( components i j y x a a a i a a x x
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Example 1: a x = 3, a y = - 4 . Find a and . 53 ) 3 / 4 arctan( 3 / 4 tan 5 4 3 2 2 2 2 x y y x a a a a a Example 2: a = 4, = 30 . Find a x , a y . j i a a a a a y x 2 46 . 3 2 2 1 4 30 sin 4 sin 46 . 3 73 . 1 2 3 2 2 3 4 30 cos 4 cos Example 3: = 30 , a y = 3 . Find a x , and a. 19 . 5 73 . 1 3 2 3 6 30 cos 6 cos 6 30 sin 3 sin sin a a a a a a x y y
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z y x k j i b    , , , , b b k b j b i b b b b b b z y x z y x 3 - Dimensional Vectors (3D) 2 2 2 y y x b b b b b
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X Y Z Right-hand rule X Y Z
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b a c b a p c q cp q cp q cp q z z y y x x p c q Vector addition Geometric: z z z y y y x x x b a c b a c b a c Algebraic: Multiplication
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Unformatted text preview: by number b a c Triangle inequality: Properties: b c a c b a c c b a c b a a b b a A vector A is given by A (3.00 m) i (4.00 m) j . The unit vector in the direction of A is: 1. (0.60 m) i (0.80 m) j 2. 0.75 i 1.00 j 3. 0.30 i 0.80 j 4. 0.60 i 0.80 j Question: Example: ? and between angle the is what , and relations e satisfy th and vectors the If 2 2 2 Q P R Q P R Q P R Q , P...
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lecture02 - by number b a c Triangle inequality:...

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