A particle is displaced from position r 1 = ( 2 i ^ + 3 j ^ − k ^ ) m to r 2 = ( 4 i ^ − j ^ + 2 k ^ ) m under the action of a constant force F = ( 3 i ^ + 2 j ^ + 4 k ^ ) N . Match the foll

Question

A particle is displaced from position r 1 ​ = ( 2 i ^ + 3 j ^ ​ − k ^ ) m to r 2 ​ = ( 4 i ^ − j ^ ​ + 2 k ^ ) m under the action of a constant force F = ( 3 i ^ + 2 j ^ ​ + 4 k ^ ) N . Match the following quantities. List - I List - II (P) Displacement vector d (1) 2 i ^ − 4 j ^ ​ + 3 k ^ m (Q) Work done by the force (2) 10 J (R) Magnitude of the force (3) 29 ​ N (S) Component of force along y-axis (4) 2 N

TestHub · Accepted Answer

The displacement vector is d = r 2 ​ − r 1 ​ = ( 4 − 2 ) i ^ + ( − 1 − 3 ) j ^ ​ + ( 2 − ( − 1 )) k ^ = 2 i ^ − 4 j ^ ​ + 3 k ^ m. Work done W = F ⋅ d = ( 3 ) ( 2 ) + ( 2 ) ( − 4 ) + ( 4 ) ( 3 ) = 6 − 8 + 12 = 10 J. Magnitude of force ∣ F ∣ = 3 2 + 2 2 + 4 2 ​ = 9 + 4 + 16 ​ = 29 ​ N. The component of force along the y-axis is the coefficient of j ^ ​ in F , which is 2 N.

List - I	List - II
(P) Displacement vector $d$	(1) $2 \hat{i} - 4 \hat{j} + 3 \hat{k}$ m
(Q) Work done by the force	(2) $10$ J
(R) Magnitude of the force	(3) $29$ N
(S) Component of force along y-axis	(4) $2$ N

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