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Question

If a,b,c are three non-coplanar vectors such that a+b+c=αd and b+c+d=βa then a+b+c+d is equal to

A
0
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B
αa
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C
βb
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D
(α+β)c
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Solution

The correct option is A 0
a+b+c=α(βabc)
(1αβ)a+(1+α)b+(1+α)c=0
1=αβ and α=1(a,b,c are non-coplanar so linearly independent)
Substitute the value α=1, we get a+b+c+d=0

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