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Question
A particle acted on by constant forces `8hat"i" + 2hat"j" - 6hat"k"` and `6hat"i" + 2hat"j" - 2hat"k"` is displaced from the point (1, 2, 3) to the point (5, 4, 1). Find the total work done by the forces
Solution
`bar"OA" = hat"i" + 2hat"j" + 3hat"k"`
`bar"OB" = 5hat"i" + 4hat"j" + hat"k"`
`bar"d" = bar"AB"`
= `bar"OB" - bar"OA"`
= `4hat"i" + 2hat"j" - 2hat"k"`
`bar"F"_1 = 8hat"i" + 2hat"j" - 6hat"k"`
And `bar"F"_2 = 6hat"i" + 2hat"j" - 2hat"k"`
`bar"F" = bar"F"_1 + bar"F"_2`
= `14hat"i" + 4hat"j" - 8hat"k"`
Work done = `bar"F" bar"d"`
= `(14hat"i" + 4hat"j" - 8hat"k")(4hat"i" + 2hat"j" - 2hat"k")`
= 56 + 8 + 16
= 80 units
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