**69. What are the x and y components of the vector that must be added to the following three vectors, so that the sum of the four vectors is zero? Due east is the+x direction, and due north is the +y direction.

 units, 60.0° south of west

  units, 35.0° south of east

 units, 23.0° north of east

 

So we want the following Equation to Hold

 

This means separately the following two equations must hold

 

 

 

So we must solve for  and

 

 

Now we need to determine the angles in terms of a standard coordinate system.  East and North are the standard +x and +y axes.  So our original three vectors become

 

 units, 60.0° south of west, south of west is third quadrant so

 

 

  units, 35.0° south of east, south of east is fourth quadrant so

 

 

 units, 23.0° north of east, north of east is first quadrant so

 

 

Now find all the components

 

 

 

 

 

 

 

 

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This page last updated on January 11, 2020