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Question
Find the torque of the resultant of the three forces represented by `- 3hat"i" + 6hat"j" - 3hat"k", 4hat"i" - 10hat"j" + 12hat"k"` and `4hat"i" + 7hat"j"` acting at the point with position vector `8hat"i" - 6hat"j" - 4hat"k"` about the point with position vector `18hat"i" + 3hat"j" - 9hat"k"`
Solution
`bar"F"_1 = - 3hat"i" + 6hat"j" - 3hat"k"`
`bar"F"_2 = 4hat"i" - 10hat"j" + 12hat"k"`
`bar"F"_3 = 4hat"i" + 7hat"j"`
`bar"F" = bar"F"_1 + bar"F"_2 + bar"F"_3`
= `5hat"i" + 3hat"j" + 9hat"k"`
`bar"OB" = 8hat"i" - 6hat"j" - 4hat"k"`
`bar"OA" = 18hat"i" + 3hat"j" - 9hat"k"`
`bar"AB" = bar"OB" - bar"OA"`
= `- 10hat"i" - 9hat"j" + 5hat"k"`
`bar"t" = bar"r" xx bar"F" = |(hat"i", hat"j", hat"k"),(-10, -9, 5),(5, 3, 9)|`
= `hat"i"(- 81 - 15) - hat"j"(- 90 - 25) + hat"k"(- 30 + 45)`
= `- 96hat"i" + 115hat"j" + 15hat"k"`
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