The angle made by resultant vector R=2underroot3i-2j with x axis is?

1 Answer
Aug 11, 2018

Given vector

#vec R=2sqrt3hati-2hatj#

Inspection reveals that resultant has positive value of #x#-coordinate
and #-ve# value of #y#-coordinate. If we draw this vector on a #xy# coordinate system, it lies in the fourth quadrant.

If #theta# is the angle between the vector and the #x#-axis, we have

#tan theta=(-2)/(2sqrt3)#
#=>tan theta=-1/(sqrt3)#
#=>theta=arctan(-1/sqrt3)#
#=>sintheta/costheta=-1/(sqrt3)#

From the unit circle reproduced below we see that for angles in the fourth quadrant we have two values for which we can have #sqrt3#. The first value in the round brackets represents #cos# and second value represents #sin# of particular angle. The required value which gives #sqrt3# in the denominator is

#theta=330^@#
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