Let O be the origin nad P, Q, R be the points such that `vec(PO)+vec(OQ)=vec(QO)+vec(OR)`. Then which one of the following is correct?

Options

A. P, Q, R are the vertices of an equilateral triangle
B. P, Q, R are the vertices of an isosceles triangle
C. P, Q, R are collinear
D. None of the above

Answer

C

Explanation

Consider `vec(PO)+vec(OQ)=vec(QO)+vec(OR)`
`rArr vec(OQ)-vec(QO)=-vec(PO)+vec(OR)`
`rArr vec(OQ)+vec(OQ)=vec(OR)+vec(OP)`
`rArr vec(OQ)=1/2(vec(OP)+vec(OR))`
Hence Q is the mid-point of P and R.
`:. P,Q, R` are collinear.