An airplane is flying toward the southeast. Consider the wind velocity vectors $$\vec w_1 = -4\mathit{\vec i}-\mathit{\vec j} \qquad \vec w_2 = \mathit{\vec i}-2\mathit{\vec j} \qquad \vec w_3 = -\mathit{\vec i}+8\mathit{\vec j}$$ $$\vec w_4 = 12\mathit{\vec i}+2\mathit{\vec j} \qquad \vec w_5 = 6\mathit{\vec i}-\mathit{\vec j}.$$ Which of the wind velocity vectors increases the plane's speed the most?
Wind ? w1 w2 w3 w4 w5

Which slows down the plane the most?
Wind ? w1 w2 w3 w4 w5