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If `l_(1), m_(1), n_(1), l_(2), m_(2), n_(2) and l_(3), m_(3), n_(3)` are direction cosines of three mutuallyy perpendicular lines then, the value of `|(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3))|` is

A

`|{:(l_(1),m_(2),n_(3)),(l_(2),m_(3),n_(1)),(l_(3),m_(1),n_(2)):}|=0`

B

`|{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}|=0`

C

`l_(1)l_(2)l_(3) + m_(1)m_(2)m_(3) + n_(1)n_(2)n_(3)=0`

D

`l_(1)l_(2)l_(3) = m_(1)m_(2)m_(3) = n_(1)n_(2)n_(3)`

Text Solution

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The correct Answer is:
B
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