Answer
$ \lt 10 \sqrt 2-50, 10 \sqrt 2 \gt $
Work Step by Step
The component form of the vector $u$ is: $ u=||u|| \lt \cos \theta_{u} , \sin \theta_{u} \gt =20 \lt \cos 40^{\circ},\sin 40^{\circ} \gt \\= \lt 10 \sqrt 2 , 10 \sqrt 2 \gt$
Now, the component form of the vector $v$ is: $ v=||v|| \lt \cos \theta_{v} , \sin \theta_{v} \gt =50 \lt \cos 180^{\circ},\sin 180^{\circ} \gt \\= \lt -50, 0 \gt$
Thus, $u+v= \lt 10 \sqrt 2 , 10 \sqrt 2 \gt+\lt -50,0 \gt = \lt 10 \sqrt 2-50, 10 \sqrt 2 \gt $
