Question

URGENT

Answer 1

Compute the components of the second vector in Cartesian coordinates. You're given the magnitude $r=7$ and direction $\theta=\frac{2\pi}3$. In Cartesian, this vector corresponds to $\langle x,y\rangle$ where

$x=r\cos\theta=7\cos\dfrac{2\pi}3=-\dfrac72$

$y=r\sin\theta=7\sin\dfrac{2\pi}3=\dfrac{7\sqrt3}2$

Then the sum of this vector with $\langle3,4\rangle$ is

$\left\langle-\dfrac72,\dfrac{7\sqrt3}2\right\rangle+\langle3,4\rangle=\left\langle-\dfrac12,4+\drac{7\sqrt3}2\right\rangle$