A small particle moves to position 5 i ^ - 2 j ^ + k ^ from its initial position 2 i ^ + 3 j ^ - 4 k ^ under the action of force 5 i ^ + 2 j ^ + 7 k ^ N . The value of work done will be ______ J .

Step-by-step solution

Work done by a constant force is given by W = Force F → · Displacement r → , where, r → = r → 2 - r → 1 Given here, r 1 → = 5 i ^ - 2 j ^ + k ^ and r → 2 = 2 i ^ + 3 j ^ - 4 k ^ So, W = F → · r → 2 - r → 1 = ( 5 i ^ + 2 j ^ + 7 k ^ ) · ( 5 i ^ - 2 j ^ + k ^ ) - ( 2 i ^ + 3 j ^ - 4 k ^ ) ⇒ W = 40   J