Answer to Question #203441 in Analytic Geometry for Master j

Question #203441

Calculate the work done by a Force of 2𝑖 βˆ’ 𝑗 βˆ’ 3π‘˜ in moving an object from (2, 1, 3) to (9, 4, 6) where displacement is in meters


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Expert's answer
2021-06-07T12:07:20-0400

Let the the object move from P(2, 1, 3) to Q(9, 4, 6) Here, the position vectors,  p​=2i +1j+3kand  q​=9i +4j+6kHence,  PQ​ = q​ βˆ’ p​ =(9i +4j+6k)βˆ’(2i +1j+3k)=7i +3j+3k F =2i βˆ’1jβˆ’3k βˆ΄ Work done = F . PQ​  =(2i βˆ’1jβˆ’3k ).(7i +3j+3k)=14βˆ’3βˆ’9=2 metersLet\space the\space the\space object\space move\space from\space P(2,\space 1,\space 3)\space to\space Q(9,\space 4,\space 6)\space \\ Here,\space the\space position\space vectors,\space \space \\ p​=2 {i} \space +1 {j} +3 {k} \\ and\space \space \\ q​=9 {i} \space +4 {j} +6 {k} \\ Hence,\space \space \\ PQ​\space =\space q​\space βˆ’\space p​ \space \\ =(9 {i} \space +4 {j} +6 {k} )βˆ’(2 {i} \space +1 {j} +3 {k} )\\ =7 {i} \space +3 {j} +3 {k} \\ \space F\space =2 {i} \space -1 {j} -3 {k} \\ \space ∴\space Work\space done\space =\space F\space .\space PQ​\\ \space \space =(2 {i} \space -1 {j} -3 {k} \space ).(7 {i} \space +3 {j} +3 {k} )\\ =14-3-9=2\space meters\\


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