The route followed by a hiker consists of three displacement vectors , , and . vector is along a measured trail and is 1550 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 41.0° east of south. similarly, the direction of vector is 29.0° north of west. the hiker ends up back where she started, so the resultant displacement is zero, or + + = 0. find the magnitudes of vector and vector .

Refer to the diagram shown below.

Define
 = unit vector in the eastern direction
 = unit vector n the northern drection.

Then the displacement vectors are
Vector #1:  
Vector #2: 
Vector #3: 

Because the vector sum of all three vector is zero, therefore
1381.1 +0.6561a - 0.891b = 0
703.7 - 0.9873a + 0.454b = 0

That is,
  0.6561a - 0.891b  = -1381.1         (1)
-0.9873a + 0.454b = -703.7        (2)

From (1), obtain
b = 0.7364a + 1550.1                 (3)
Substitute (3) into (2).
-0.9873a + 0.454(0.7364a + 1550.1) = - 703.7
-0.653a = -1407.4
a = 2155.3 mles
From (3), obtain
b = 3137.2 mles

The magnitudes of the two displacement vectors are
2155.3 miles and 3137.2 miles.

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Answerthe energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.explanationwe define electric potential as the ratio electric potential energy to the charge,    then the following gives us the potential difference,      the formula  may be on your formula sheet.the change in electric potential energy would be the energy that would needed to move it from point a to point b. solving for that, we get    using q = 8.00  × 10⁻¹⁹ c and  δv = 2.00 v, we get    the energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.