a, b, c are 3 vectors such that a+ b+ c= 0, | a|=1, | b|=2, | c|=3, then a b+ b c+ c a is … · questionr

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Question 361 of 379EasyMCQ

\vec a,\vec b,\vec c

are 3 vectors such that

\vec a+\vec b+\vec c=\vec 0

,

|\vec a|=1

,

|\vec b|=2

,

|\vec c|=3

, then

\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a

is equal to:

Solutions · 1

Official solution

|\vec a+\vec b+\vec c|^2=0 \implies |\vec a|^2+|\vec b|^2+|\vec c|^2+2(\vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a)=0

\[1+4+9+2(\ldots)=0 \implies \vec a\cdot\vec b+\vec b\cdot\vec c+\vec c\cdot\vec a=\frac{-14}2=-7\]

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