A body of mass 4 kg experiences two forces \(\rm \vec F_1=5\hat i+8\hat j+7\hat k\ and\ \vec F_2=3\hat i-4\hat j-3\hat k\) The acceleration acting on the body is :

Concept:

• Force is an external agent capable of changing a body's state of rest or motion.
• It has a magnitude and a direction. 
• Force is a vector quantity. Its unit is Newton N.
• Dimension LT^-2
• The net force is the vector sum of all the forces. That is, the net force is the resultant of all the forces; it is the result of adding all the forces together as vectors.

Calculation:

Here, \(\rm \vec F_1=5\hat i+8\hat j+7\hat k\ and\ \vec F_2=3\hat i-4\hat j-3\hat k\)

Since, F_net = F₁ + F₂ and F = ma

_⇒ Fnet = \(8\hat i + 4\hat j + 4\hat k\)

⇒ a =  F_net / m =  (\(8\hat i + 4\hat j + 4\hat k\) ) / 4

⇒ a = 2î + ĵ + k̂

∴ The acceleration acting on the body is 2î + ĵ + k̂

Hence option 3) is the correct option.