Question

Calculate the work done by a Force of 2𝑖 − 𝑗 − 3𝑘 in moving an object from (2, 1, 3) to (9, 4, 6) where displacement is in meters

Answer 1

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