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\vec{a},\vec{b},\vec{c},\vec{d} are vectors then (\vec{a}\times \vec{b})\times (\vec{c}\times \vec{d} )  equals

Option: 1

[\vec{a}\: \: \vec{c}\: \: \vec{d}\: \:]\vec b + [\vec{b}\: \vec{c}\: \vec{d}] \vec a


Option: 2

[\vec{a}\: \: \vec{c}\: \: \vec{d}\: \:]\vec b - [\vec{b}\: \vec{c}\: \vec{d}] \vec a


Option: 3

[\vec{d}\: \: \vec{a}\: \: \vec{b}\: \:]\vec c + [\vec{a}\: \vec{b}\: \vec{c}] \vec d


Option: 4

None of these


Answers (1)

best_answer

(\vec a \times \vec b )\times ( \vec c \times \vec d)= -[(\vec c \times \vec d )\times ( \vec a \times \vec b)]= - [((\vec c \times \vec d ).\vec b)\vec a - ((\vec c \times \vec d ).\vec a )\vec b]

=[\vec{a}\: \: \vec{c}\; \; \vec{d}]\vec b - [ \vec{b}\: \: \vec{c}\: \: \vec{d}] \vec a

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Anam Khan

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