hibbeler chapter4 솔루션 다운
hibbeler chapter4 솔루션 다운
hibbeler chapter4 솔루션
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 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 +
자료출처 : http://www.ALLReport.co.kr/search/Detail.asp?pk=11048326&sid=knp868group1&key=
[문서정보]
문서분량 : 40 Page
파일종류 : PDF 파일
자료제목 : hibbeler chapter4 솔루션
파일이름 : hibbeler_chapter4.pdf
키워드 : 12,hibbeler,chapter4,솔루션
자료No(pk) : 11048326
hibbeler chapter4 솔루션
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 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 +
자료출처 : http://www.ALLReport.co.kr/search/Detail.asp?pk=11048326&sid=knp868group1&key=
[문서정보]
문서분량 : 40 Page
파일종류 : PDF 파일
자료제목 : hibbeler chapter4 솔루션
파일이름 : hibbeler_chapter4.pdf
키워드 : 12,hibbeler,chapter4,솔루션
자료No(pk) : 11048326
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