If-the-constant-forces-2i-5j-6k-and-i-2j-k-act-on-a-particle-due-to-which-it-is-displaced-from-a-point-A-4-3-2-to-a-point-B-6-1-3-then-the-work-done-by-the-forces-is-

Question Number 58056 by Salomon M. last updated on 17/Apr/19

If the constant forces 2 i - 5 j + 6 k and

- i + 2 j - k act on a particle due to which

it is displaced from a point A (4, - 3, - 2)

to a point B (6, 1, - 3), then the work

done by the forces is

Answered by tanmay last updated on 17/Apr/19

O \vec{A} = 4 i - 3 j - 2 k

O \vec{B} = 6 i + j - 3 k

d i s p l a c e m e n t = A \vec{B} = O \vec{B} - O \vec{A}

A \vec{B} = (6 i + j - 3 k) - (4 i - 3 j - 2 k)

A \vec{B} = 2 i + 4 j - k

{\vec{F}}_{1} + {\vec{F}}_{2} = (2 i - 5 j + 6 k) + (- i + 2 j - k)

{\vec{F}}_{1} + {\vec{F}}_{2} = i - 3 j + 5 k

W = ({\vec{F}}_{1} + {\vec{F}}_{2}) . (A \vec{B})

= (i - 3 j + 5 k) . (2 i + 4 j - k)

= 2 \times 1 + (- 3) \times 4 + 5 \times (- 1)

= 2 - 12 - 5

= - 15 u n i t

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