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


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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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