7.2. Operations with Vectors http://www.ck12.org
- An airplane is flying at a bearing of 270◦at 400 mph. A wind is blowing due south at 30 mph. Does this cross
wind affect the plane’s speed?
Answers:
The angle between−−→b and−→a is 53◦because in the diagram−→b is parallel to−−→b so you can use the fact
that alternate interior angles are congruent. Since the magnitudes of vectors−→a and−−→b are known to be 5
and 9, this becomes an application of the Law of Cosines.y^2 = 92 + 52 − 2 · 9 · 5 ·cos 53◦
y≈ 7. 2- Do multiplication first for each term, followed by vector subtraction.
3 ·−→v− 2 ·−→u = 3 ·< 2 , 5 >− 2 ·<− 1 , 9 >
=< 6 , 15 >−<− 2 , 18 >
=< 8 ,− 3 >- Since the cross wind is perpendicular to the plane, it pushes the plane south as the plane tries to go directly
east. As a result the plane still has an airspeed of 400 mph but the groundspeed (true speed) needs to be calculated.
4002 + 302 =x^2
x≈ 401Practice
Consider vector−→v =< 1 , 3 >and vector−→u =<− 2 , 4 >.