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 $y=2sin pi=0$

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