The work done by the force is 64 kJ , The angle between F and d is 42.46 degree.
A vector is an object that has both magnitude and direction.
It is given that
force F→=(8.0i^+9.6j^+11.2k^)kN
mass = 95 g
If the displacement of the object is d→=(3.8i^+3.5j^)m,
work done = ?
Work Done = (Force ) * Distance
Work done = (8.0i^+9.6j^+11.2k^)*(3.8i^+3.5j^)
Work Done = 64 kJ
Work Done is a scalar quantity
The angle between F and d is
cos [tex]\rm \theta[/tex] = (vector Fd)/(Magnitude of Fd)
[tex]\rm F = \sqrt{8^2+9.6^2+11.2^2}\\\\\\F= 16.78\\\\\\d = \sqrt{3.8^2+ 3.5^2}\\\\\\d = 5.17[/tex]
cos [tex]\rm \theta[/tex] = 64 / (16.78*5.17)
cos [tex]\rm \theta[/tex] = 0.7377
[tex]\rm \theta[/tex] = 42.46 degree
The angle between F and d is 42.46 degree.
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