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 A0 Given,a+b+c=αd⇒b+c=αd−a−−−−−−(i)b+c+d=βa⇒b+c=βa−d−−−−−−(ii)comparebothequ(i)&(ii)αd−a=βa−d[→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.