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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
Given,a+b+c=αdb+c=αda(i)b+c+d=βab+c=βad(ii)comparebothequ(i)&(ii)αda=βad[d=a(α+1)d=(β+1)aif,α=1,β=1then,valueis0=0,and,equna+b+c+d=o,itmeansifa+b+c+disequalto0.sothatwecansaytheconditioniscorrect.

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