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The route followed by a hiker consists of three displacement vectors  ,  , and  . Vector  is along a measured...

The route followed by a hiker consists of three displacement vectors  ,  , and  . Vector  is along a measured trail and is 2670 m in a direction 27.0 ° north of east. Vector  is not along a measured trail, but the hiker uses a compass and knows that the direction is 34.0 ° east of south. Similarly, the direction of vector  is 42.0 ° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or  +  +  = 0. Find the magnitudes of (a) vector  and (b) vector  .

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