How Is the Angle Calculated Between Displacement Vectors in Navigation?

AI Thread Summary
To calculate the angle between displacement vectors in navigation, the discussion focuses on a walking pattern consisting of 6.6 km north, 3.0 km west, and 7.0 km south, resulting in a straight-line distance of 3.02 km from the starting point to the final point. The formula provided for finding the angle, cos(α) = (u·v)/(|u||v|), involves using the dot product of the two displacement vectors and their magnitudes. The initial calculation of 7.59 degrees for the angle was incorrect, prompting a request for assistance in solving for the correct angle. Participants are encouraged to clarify any points if needed. The discussion emphasizes the importance of accurately applying vector mathematics to determine the angle between displacement vectors.
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A person walks in the following pattern: 6.6 km north, then 3.0 km west, and finally 7.0 km south. How far and in what direction would a bird fly in a straight line from the same starting point to the same final point?

I found that the distance would be 3.02 km. My problem is trying to find the angle. I came up with an angle of 7.59 degrees but that was not right. Please, any help would be appreciated.
 
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Try using this formula: cos(\alpha) = (u(dot)v)/(|u||v|)

Sorry I am not very good with latex but it says that the cosine of alpha is equal to the dot product of the two vectors that you need the angle between over the magnitude of of one of your vectors times the other. So with your info solve for alpha.
If you need clarification please ask.
 

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