$a_{1}=10 \mu m, a_{2}=4 \mu m$ and $a_{3}=7 \mu m$

and the phase difference between $1\, st$ and $2\, nd$ wave is $\frac{\pi}{2}$ and that between $2\, nd$

and $3\,rd$ wave is $\frac{\pi}{2} .$ Therefore, phase difference between $1\, st$ and $3\, rd$ is $\pi$.

Combining $1st$ with $3rd,$ their resultant amplitude is given by

$A_{1}^{2}=a_{1}^{2}+a_{3}^{2}+2 a_{1} a_{3} \cos \varphi$

or $A_{1}=\sqrt{10^{2}+7^{2}+2 \times 10 \times 7 \cos \pi}$

$=\sqrt{100+49-140}$

$=\sqrt{9}=3 \mu m$ in the direction of first.

Now combining this with $2\, nd$ wave we have, the resultant amplitude

$A^{2}=A_{1}^{2}+a_{2}^{2}+2 A_{1} a_{2} \frac{\cos \pi}{2}$

or $A=\sqrt{3^{2}+4^{2}+2 \times 3 \times 4 \cos 90^{\circ}}=\sqrt{9+16}$

$=5 \mu m$