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Ilyasssssss
@Ilyasssssss
July 2022
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a, b и с единичные векторы. если a+b+c=0 то найдите a*b+b*c+c*a
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nabludatel00
Verified answer
A*b + b*c + c*a = (1/2)*( 2ab + 2bc + 2ac) = (1/2)*( (ab+bc) + (ab+ac) + (bc+ac) ) = (1/2)*( b*(a+c) + a*(b+c) + c*(b+a) ) = W.
Из условия a+b+c = 0, получим
a+c = -b;
b+c = -a;
b+a = -c;
Тогда W = (1/2)*( b*(-b) + a*(-a) + c*(-c) ) = V.
Т.к. векторы единичные, то получаем
V = (1/2)*( -1 -1 -1) = -3/2 = -1,5.
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Answers & Comments
Verified answer
A*b + b*c + c*a = (1/2)*( 2ab + 2bc + 2ac) = (1/2)*( (ab+bc) + (ab+ac) + (bc+ac) ) = (1/2)*( b*(a+c) + a*(b+c) + c*(b+a) ) = W.Из условия a+b+c = 0, получим
a+c = -b;
b+c = -a;
b+a = -c;
Тогда W = (1/2)*( b*(-b) + a*(-a) + c*(-c) ) = V.
Т.к. векторы единичные, то получаем
V = (1/2)*( -1 -1 -1) = -3/2 = -1,5.