If A,B,C and D are {3,7,4),(5,-2,-3),(-4,5,6) and (1,2,3) respectively, then the value 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)hatk`
` = 2hati - 9hatj - hatk`
`AC = (-4 - 3)hati + (5- 7) hatj + (6 - 4)hatk`
`= -7 hati - 2hatj + 2hatk`
and `AD = (1-2)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,-1),(,-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 .