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Question

If a+b+c=αd and b+c+d=βa and a,b,c are non-coplanar vectors , then show that a+b+c+d=0

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Solution

a+b+c=αd [ Given ]

b+c=αda ------ ( 1 )

b+c+d=βa [ Given ]

b+c=βad ------ ( 2 )

αda=βad [ From ( 1 ) and ( 2 ) ]

αd+d=βa+a

(α+1)d=(β+1)a ----- ( 3 )

da

Now, α=1 and β=1

Equation ( 3 ) will be 0.

a+b+c+d=0

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