If four vectors →a,→b,→c,→d are coplanar then (→a×→b)×(→c×→d) is equal to
A
[→a→b→d]→c
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B
[→a→b→c]→d
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C
[→b→c→d]→a
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D
null vector
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Solution
The correct option is D null vector (→a×→b)×(→c×→d)=[→a→b→d]→c−[→a→b→c]→d
As, all vectors are coplanar, their scalar tripple product will be zero.
So,(→a×→b)×(→c×→d)=→0 is a null vector.