Answer :
Compute the components of the second vector in Cartesian coordinates. You're given the magnitude [tex]r=7[/tex] and direction [tex]\theta=\frac{2\pi}3[/tex]. In Cartesian, this vector corresponds to [tex]\langle x,y\rangle[/tex] where
[tex]x=r\cos\theta=7\cos\dfrac{2\pi}3=-\dfrac72[/tex]
[tex]y=r\sin\theta=7\sin\dfrac{2\pi}3=\dfrac{7\sqrt3}2[/tex]
Then the sum of this vector with [tex]\langle3,4\rangle[/tex] is
[tex]\left\langle-\dfrac72,\dfrac{7\sqrt3}2\right\rangle+\langle3,4\rangle=\left\langle-\dfrac12,4+\drac{7\sqrt3}2\right\rangle[/tex]