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마케팅전문가

hibbeler chapter4 해결책

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작성일18-06-11 16:51

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솔루션/기계설계

정역학 , hibbeler chapter4 솔루션기계설계솔루션 , 12


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정역학





Engineering Mechanics - Statics

Chapter 4

Problem 4-1 If A, B, and D are given vectors, prove the distributive law for the vector cross product, i.e., A × ( B + D) = ( A × B) + ( A × D). Solution: Consider the three vectors; with A vertical. Note triangle obd is perpendicular to A. od = A × ( B + D) = A

(

B + D ) sin ( θ 3 )

ob = A × B = A B sin ( θ 1 ) bd = A × D = A B sin ( θ 2 ) Also, these three cross products all lie in the plane obd since they are all perpendicular to A. As noted the magnitude of each cross product is proportional to the length of each side of the triangle. The three vector cross - products also form a closed triangle o`b`d` which is similar to …(투비컨티뉴드 ) triangle obd. Thus from the figure, A × ( B + D) = A × B + A × D Note also, A = Axi + Ayj + A zk B = Bxi + B yj + B zK D = Dxi + Dyj + Dzk j k ? ? i ? ? Ay Az ? A × ( B + D) = ? Ax ?B + D B + D B + D ? x y y z z? ? x = (QED)

?Ay( Bz + Dz) ? Az( By + Dy)? i ? ?Ax( Bz + Dz) ? Az( Bx + Dx)? j +

12,기계설계,솔루션
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hibbeler chapter4 해결책




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