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A line L(1) with direction ratios -3,2,4...

A line `L_(1)` with direction ratios `-3,2,4` passes through the point A(7,6,2) and a line `L_(2)` with directions ratios 2,1,3 passes through the point B(5,3,4). A line `L_(3)` with direction ratios `2,-2,-1` intersects `L_(1)` and `L_(3)` at C and D, resectively.
The volume of parallelopiped formed by `vec(AB), vec(AC)` and `vec(AD)` is equal to

A

140

B

138

C

134

D

130

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Verified by Experts

The correct Answer is:
B
Volume `[bar(AB)bar(AC)bar(AD)]=|{:(2,3,-2),(6,-4,-8),(0,2,-5):}|`=138
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