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imagin12
@imagin12
July 2022
1
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Даю много баллов!
В тетраэдре ABCD на медиане CC1 грани ABC взята точка Р так,что СР: РС1= 4:1 . Выразите вектор DP через векторы a= DC b=DA c=DB
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sedinalana
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AB=DB-DA=c-b
AC1=1/2*AB=1/2*c-1/2*b
AC=DC-DA=a-b
CC1=AC1-AC=1/2*c-1/2*b-a+b=1/2*c+1/2*b-a
CP=4/5*CC1=4/10*C+2/5*b-4/5*a
DP=DC+CP=a+4/10*c+2/5*b-4/5*a=1/5*a+2/5*b+4/10*c
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Verified answer
AB=DB-DA=c-bAC1=1/2*AB=1/2*c-1/2*b
AC=DC-DA=a-b
CC1=AC1-AC=1/2*c-1/2*b-a+b=1/2*c+1/2*b-a
CP=4/5*CC1=4/10*C+2/5*b-4/5*a
DP=DC+CP=a+4/10*c+2/5*b-4/5*a=1/5*a+2/5*b+4/10*c