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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.A. 91B. 94C. 92D. 93 |
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Answer» Correct Answer - C 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 . |
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