Let a→,b→and c→ be three unit vectors such that a→$$+b$$→$$+c$$→$$=0$$→. If λ$$=a$$→.b→$$+b$$→.c→$$+c$$→.a→and then d→$$=a$$→×b→$$+b$$→×c→$$+c$$→×a→the ordered pair,λ,d→ is equal to:

Correct option is 4−32,3a→×b→

Questions

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$ . If $λ = \vec{a} . \vec{b} + \vec{b} . \vec{c} + \vec{c} . \vec{a}$ and then $\vec{d} = \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ the ordered pair, $(λ, \vec{d})$ is equal to:

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32,3b→×c→

32,3a→×c→

−32,3c→×b→

−32,3a→×b→

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detailed solution

Correct option is D

a→+b→+c→2=03+2a→.b→+b→.c→+c→.a→=0a→.b→+b→.c→+c→.a→=−32⇒λ=−32d→=a→×b→+b→×−a→−b→+−a→−b→×a→=a→×b→+a→×b→+a→×b→d→=3a→×b→

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Let a→,b→and c→ be three unit vectors such that a→+b→+c→=0→. If λ=a→.b→+b→.c→+c→.a→and then d→=a→×b→+b→×c→+c→×a→the ordered pair,λ,d→ is equal to:

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