For non -zero vectors →a,→b,→c(→a×→b).→c=∣∣→a∣∣∣∣∣→b∣∣∣∣∣→c∣∣ holds if
A
→a.→b=0,→b.→c=0,→c.→a≠0
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B
→a.→b≠0,→b.→c=0,→c.→a=0
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C
→a.→b=0,→b.→c≠0,→c.→a=0
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D
→a.→b=0,→b.→c=0,→c.→a=0
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Solution
The correct option is C→a.→b=0,→b.→c=0,→c.→a=0 (→a×→b).→c represents the volume of the parallelopiped whose coterminous edges are →a,→b,→c and this ∣∣→a∣∣∣∣∣→b∣∣∣∣∣→c∣∣ it it is rectangular, i.e. if →a.→b=0,→b.→c=0,→c.→a=0