If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a), then vec(a)+vec(b)+vec(c )+vec(d) is equal to

If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)

1.	If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a), then vec(a)+vec(b)+vec(c )+vec(d) is equal to
Answer» `vec(0)` `alphavec (a)` `betavec(B)` `(alpha-beta)vec(c )` SOLUTION :`because vec(a)+vec(b)+vec(c)=alphavec(d) " and " vec(b)+vec(c)+vec(d)=betavec(a)impliesvec(a)+vec(b)+vec(c)=alphavec(d) " and " vec(d)=betavec(a)-vec(b)-vec(c)` `impliesvec(a)+vec(b)+vec(c)=alpha(betavec(a)-vec(b)-vec(c))IMPLIES(1-alphabeta)vec(a)+(1+alpha)vec(b)+(1+alpha)vec(c)=vec(0)` `impliesalphabeta=1,alpha=-1{because vec(a),vec(b),vec(c)" arenon COPLANAR"}implies alpha=beta=-1` `becausevec(a)+vec(b)+vec(c)=alphavec(d)impliesvec(a)+vec(b)+vec(c)+vec(d)=vec(0)`

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If vec(a),vec(b),vec(c )are three non coplanar vector such that vec(a)+vec(b)+vec(c )=alphavec(d) and vec(b)+vec(c )+vec(d)=betavec(a), then vec(a)+vec(b)+vec(c )+vec(d) is equal to

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