If A,B,C and D are {3,7,4),(5,-2,-3),(-4,5,6) and (1,2,3) respectively, then the volume of the parallelopiped with AB, AC and AD as the co-terminus edges, is . . . Cubic units.

Options

A. 91
B. 94
C. 92
D. 93

Answer

C

Explanation

We have `AB=(5,-3)hati+(-2-7)hatj+(3-4)hattk`
`=2hati-9j-hatk`
`AC=(4--3)hati+(5-7)hatj+(6-4)hatk`
`=-7hati-2hatj+2hatk`
and `AD=(1-3)hati+(2-7)hatj+(3-4)hatk`
`=-2hati-5hatj-hatk`
`therefore`Volume of the parallelopiped with AB, AC and AD on the co-terminus edges
`=|[AB AC AD]|=|(2,-9,-1),(-7,-2,2),(-2,-5,-1)|`
`=|2(2+10)+9(7+4)-1(35-4)|`
`=|2(12)+9(11)-1(31)|=|(24+99-31)|`
`=|92|=92` cubic units