The position vectors of the points A,B, and C are `hati+2hatj-hatk, hati+hatj+hatk`, and `2hati+3hatj+2hatk` respectively. If A is chosen as the origin, then the position vectors B and C are

Options

A. `veci+2hatk, hati+hatj+3hatk`
B. `hatj+2hatk, hati+hatj+3hatk`
C. `-hatj+2hatk, hati-hatj+3hatk`
D. `-hatj+2hatk,hati+hatj+3hatk`

Answer

D

Explanation

`vec(OA) =hati+2hatj-hatk, vec(OB)= hati+hatj+hatk, vec(OC) = 2hati+3hatj+2hatk`
Position vector of B w.r.t. origin at A is
`vec(AB) = vec(OB)-vec(OA) =-hatj+2hatk`
Position vector of C w.r.t. origin at A is
`vec(AC) = vec(OC) -vec(OA) = hati+hatj+3hatk`