Lecture03_Vectors_Review

Lecture03_Vectors_Review - P7.3-47: Given | F |= 30 N r d...

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18 Work done by w (gravity force) = w . d = 0 ( w d ) Work done by F (applied force) = F . d = |F|.|d| cos θ ( d // F ) = 150 N.m m d N F > =< = 3 , 4 30 || || r P7.3-47 : Given weight
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19 Properties of Dot Product ± a . b = 0 if a = 0 or b = 0 ± a . b = b . a (commutative law) ± a . ( b + c )= a . b + a . c (distributive law) ± a . ( k b )= ±( k a ) . b = k ( a.b ) k a scalar ± a . a 0 ± a . a = || a || 2 ± For nonzero vectors a and b (i) a . b > 0 if and only if θ is acute (ii) a . b < 0 if and only if θ is obtuse, and (iii) a . b = 0 if and only of if cos θ =0 ( Orthogonal vectors ) Theorem 7.1 Criterion for Orthogonal Vectors Two nonzero vectors a and b are orthogonal if and only if a . b
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Angle Between Two Vectors: || || || || || || || || cos 3 3 2 2 1 1 b a b a b a b a b a b a + + = = r r θ 27 2 14 cos = o 9 . 44 77 . 0 9 42 cos 1 = ± Example Find the angle between a = 2 i +3 j + k & b = - i +5 j + k =14, Solution:
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Lecture03_Vectors_Review - P7.3-47: Given | F |= 30 N r d...

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