Find the work done by a force $\mathbf { F } = \mathbf { i } + 5 \mathbf { j } + 7 \mathbf { k }$ that moves an object from the point $( 3,0,5 )$ to the point $( 7,5,10 )$ along a straight line. The distance is measured in meters and the force in newtons.
A) $64 \mathrm {~J}$
B) $74 \mathrm {~J}$
C) $84 \mathrm {~J}$
D) $94 \mathrm {~J}$
E) $104 \mathrm {~J}$

Question

Quizplus · Accepted Answer

The work done by a force is given by the dot product of the force and the displacement vector. The displacement vector is $( 7,5,10 ) - ( 3,0,5 ) = ( 4,5,5 )$. The dot product of the force and the displacement vector is $( 1 + 5 + 7 ) \cdot ( 4 + 5 + 5 ) = 64$. Therefore, the work done by the force is $64 \mathrm {~J}$.

Find the Work Done by a Force F=i+5j+7k\mathbf { F } = \mathbf { i } + 5 \mathbf { j } + 7 \mathbf { k }F=i+5j+7k

Find the Work Done by a Force $\mathbf { F } = \mathbf { i } + 5 \mathbf { j } + 7 \mathbf { k }$