Question

A force F = 4i+2j+k acts on a particle and the particle moves from the point A to B. If displacement AB = (2,2,1) then the work done by the force F is . A. 13 B. 12 C. -13 D. 25​

Answer 1

Answer:

13

Step-by-step explanation:

Force F = 4i + 2j + k

Displacement AB = (2, 2, 1) = 2i + 2j + k

Work done = force . displacement

= (4i + 2j + k).(2i + 2j + k)

= 8 + 4 + 1

= 13

Multiplication of the vectors:

=> (4i + 2j + k).(2i + 2j + k)

=> 8i² + 8ij + 4ik + 2ij + 2j² + 2jk + 2ik + 2kj + k²

Since, ij = ji = ik = ki = jk = kj = 0 & i² = j² = k² = 1

=> 8i² + 4j² + k²

=> 8 + 4 + 1

=> 13