Find the work done by the force $F = 2 i + j + k$ if its point of application moves in a straight line from the point $P (1, 1, 1)$ to the point $Q (2, 1, 3)$ .

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Solution

$F = 2^i +^j +^k$
$\Rightarrow P =^i +^j +^k$
$\Rightarrow Q = 2^i +^j + 3^k$
$\Rightarrow S = P Q = (2^i +^j + 3^k) - (^i +^j +^k)$ $=^i + 2^k$
Work done $= ¯ ¯¯ ¯ F . ¯ ¯¯ ¯ S$
$= 2^i +^j +^k .2^i + 2^k$
$= 2 + 2 = 4$ units.

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Find the work done by the force F=2i+j+k if its point of application moves in a straight line from the point P(1,1,1) to the point Q(2,1,3).

F=2^i+^j+^k ⇒P=^i+^j+^k ⇒Q=2^i+^j+3^k ⇒S=PQ=(2^i+^j+3^k)−(^i+^j+^k)=^i+2^kWork done =¯¯¯¯F.¯¯¯¯S =2^i+^j+^k.2^i+2^k=2+2=4 units.

Find the work done by the force $F = 2 i + j + k$ if its point of application moves in a straight line from the point $P (1, 1, 1)$ to the point $Q (2, 1, 3)$ .

$F = 2^i +^j +^k$
$\Rightarrow P =^i +^j +^k$
$\Rightarrow Q = 2^i +^j + 3^k$
$\Rightarrow S = P Q = (2^i +^j + 3^k) - (^i +^j +^k)$ $=^i + 2^k$
Work done $= ¯ ¯¯ ¯ F . ¯ ¯¯ ¯ S$
$= 2^i +^j +^k .2^i + 2^k$
$= 2 + 2 = 4$ units.