Figure shows three vectors `vec(a), vec(b)` and `vec(c)`, where R is the midpoint of PQ. Then which of the following relations is correct?

Options

A. `vec(a)+vec(b)=2vec(c)`
B. `vec(a)+vec(b)=vec(c)`
C. `vec(a)-vec(b)=2vec(c)`
D. `vec(a)-vec(b)=vec(c)`

Answer

A

Explanation

`vec(a)=vec(c)+vec(RP)` and `vec(b)=vec(c)+vec(RQ)` but `vec(RP)=-vec(RQ)`
`rArr vec(a)+vec(b)=2vec(c)+vec(RP)+vec(RQ) rArr vec(a)+vec(b)=2vec(c)`