Please answer and explain. Thanks! The route followed by a hiker consists of thr

Question

Please answer and explain. Thanks! The route followed by a hiker consists of three displacement vectors A middot B, and C. Vector A is along a measured trail and is 1740 m in a direction 23.0 degree north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 31.0 degree east of south. Similarly, the direction of vector C is 27.0 degree north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0. Find the magnitudes of (a) vector B and (b) vector C (a) Number Units (b) Number Units

Explanation / Answer

given the three displacement vectors of the hike of a hiker
A = 1740 (cos(23)i + sin(23)j) [ here i is unit vector along east and j is unit vector along north]
B = |B|(sin(31)i - cos(31)j)
C = |C|(-cos(27)i + sin(31)j)
|B| and |C| are unknown quantities

but A + B + C = 0

a) using vector addition
   A + B + C = 0
   1740 (cos(23)i + sin(23)j) + |B|(sin(31)i - cos(31)j) + |C|(-cos(27)i + sin(27)j) = 0
       adding respective components we get
       i(1601.678 + |B|0.515 - |C|0.891) + j(679.872 - |B|0.857 + |C|0.453) = 0
       comparing coefficients
       1601.678 + |B|0.515 - |C|0.891 = 0
       |B| = |C|0.891 - 1601.678
       679.872 - |B|0.857 + |C|0.453 = 0
       679.872 - (|C|0.891 - 1601.678)0.857 + |C|0.453 = 0
       -0.310587|C| + 2052.51 = 0
       |C| = 6621
       |B| = 4297.633
   a. |B| = 4297.633 m
   b. |C| = 6621 m

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