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If theta is the acute angle between two ...

If `theta` is the acute angle between two intersecting straight lines, one having direction cosines `l_(1),m_(1),n_(1)` and the other having direction cosines `l_(2),m_(2),n_(2)` then `sin^(2)theta`=

A

`(l_(1)+l_(2)+l_(3))^(2)+(m_(1)+m_(2)+m_(3))^(2)`

B

`(l_(1)m_(2)+l_(2)m_(1))^(2)+(m_(1)n_(2)+m_(2)n_(1))^(2)+(n_(1)l_(2)+n_(2)l_(1))^(2)`

C

`(l_(1)m_(2)-l_(2)m_(1))^(2)+(m_(1)n_(2)-m_(2)n_(1))^(2)+(n_(1)l_(2)-n_(2)l_(1))^(2)`

D

none of these

Text Solution

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The correct Answer is:
C
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