What are the components of the vector between the origin and the polar coordinate #(2, pi)#?

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Answer 1 · 2016-05-26T05:25:45

#-2hati+0hatj#

OR

#(-2,0)#

If #(r.theta)# be the polar coordinate of a point in X-Y plane the position vector represented by the point is given by:

#vecr=hatircostheta+hatjrsintheta#
Here given #r=2 and theta=pi#

#:.vecr=hati*2*cospi+hatj*2*rsinpi#
Insurting #cospi=-1 and sinpi=0#

#vecr=hati*2(-1)+hatj*2*0=-2hati#

An easier way:

#x=rcos theta# and #y=rsin theta#

#x=2cos pi=-2# and #y=2sin pi=0#