Question

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

Answer 1

`-2hati+0hatj`

OR

`(-2,0)`

Explanation:

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`