# Vector problem involving velocity and wind

A 100-meter dash is run on a track in the direction of $$\vec{v} = 2\vec{e_{1}}+6\vec{e_{2}}$$. The wind velocity $$\vec{w}$$ is 5$$\vec{e}_{1}+\vec{e_{2}}$$ km/h. The rules say that a legal wind speed measured in teh direction of the dash must not exceed 5 km/h. Will the race results be disqualified due to an illegal wind?

I am unsure how to start this problem, any help would be great. I think that I must find the speed of the wind in that direction first, so finding that vector and then finding the magnitude of that vector. But I don't know how to find that vector.

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#### fresh_42

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2018 Award
If the wind speed is 5 km/h in any given direction, then it has to be less in a particular direction. So it cannot exceed 5 km/h in the track's direction.

"Vector problem involving velocity and wind"

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