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**Hint:**Whenever a body is acted by some force it gets accelerated which in mathematical form it’s called Newton’s second law of motion as $F = ma$ here, we will find the net force acting on the body and its direction then will find the net acceleration of the body.

**Complete step by step answer:**

Let us find the net magnitude of forces ${F_1}$ and ${F_2}$ which are perpendicular to each other and this net force be written as ${F_{12}}$ so,

${F_{12}} = \sqrt {{F^2} + {F^2}} $

${F_{12}} = \sqrt 2 F$ Which will be in direction just opposite to that of ${F_3}$ .

Now, two forces acting on the body of mass m respectively ${F_{12}} = \sqrt 2 F$ and ${F_3} = F$.

Both forces are in opposite direction,

Hence net force act on the body of mass $m$ is,

${F_{net}} = \sqrt 2 F - F$

$\Rightarrow {F_{net}} = (\sqrt 2 - 1)F$

Now, let us assume that net acceleration is denoted by $a'$ then by newton’ second law we have:

$(\sqrt 2 - 1)F = ma'$

We also know that, $F = ma$ put this value in above equation, we get,

$(\sqrt 2 - 1)a = a'$

Net acceleration is $a' = (\sqrt 2 - 1)a$

**Hence, the correct option is A.**

**Note:**It should be remembered that, Force is a vector quantity and its added always using vector algebra which is given as ${F_{net}} = \sqrt {{F_1}^2 + {F_2}^2 + 2{F_1}{F_2}\cos \theta } $ and the direction of two equal vectors resultant is in the middle of the angle between them. And it can also be calculated with the general formula $\tan \beta = \dfrac{{{F_2}\sin \theta }}{{{F_1} + {F_2}\cos \theta }}$.

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