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Let overline(lambda)=overline(a)times(ov...

Let `overline(lambda)=overline(a)times(overline(b)+overline(c)), overline(mu)=overline(b)times(overline(c)+overline(a)), overline(gamma)=overline(c)times(overline(a)+overline(b))`, then

A

`overline(lambda)+overline(mu)=overline(gamma)`

B

`overline(lambda), overline(mu), overline(gamma)` are coplanar

C

`overline(lambda)+overline(gamma)=2overline(mu)`

D

`overline(lambda)+overline(gamma)=overline(mu)`

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The correct Answer is:
B
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[[overline(a), overline(b), overline(a)timesoverline(b)]]=

overline(a)*((overline(a)+overline(b)+overline(c))times(overline(b)+overline(c)))=

[[overline(a)-overline(b), overline(b)-overline(c), overline(c)-overline(a)]]=

[[overline(a)+overline(b), overline(b)+overline(c), overline(c)+overline(a)]]=

If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , where overline(a), overline(b), overline(c) are three non-coplanar vectors, then (overline(a)-overline(b)-overline(c))*overline(p)-(overline(b)-overline(c)-overline(a))*overline(q)-(overline(c)-overline(a)-overline(b))*overline(r)=

If overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , where overline(a), overline(b), overline(c) are three non-coplanar vectors, then (overline(a)+overline(b)+overline(c))*(overline(p)+overline(q)+overline(r))=

|[overline(a)*overline(a), overline(a)*overline(b)], [overline(a)*overline(b), overline(b)*overline(b)]|=

[[overline(a), overline(b)+overline(c), overline(c)+overline(b)+overline(a)]]=

If overline(c)=3overline(a)-2overline(b) , then [[overline(a), overline(b), overline(c)]]=

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