Question

For question 1A-4 a) Let P and Q be two points in space, and X the midpoint of the line segment PQ. Let O be an arbitrary fixed point; show that as vectors, OX = 1/2(OP + OQ).

I am not sure how to follow the solution which is OX = OP + PX = OP + 1/2(PQ) = OP + 1/2(OQ−OP) = 1/2(OP + OQ).

Answer 1

\(\vec {OX} = \vec {OP} + \vec {PX} \)
\(= \vec {OP} + \frac{1}{2} \vec {PQ} \)
\(= \vec {OP} + \frac{1}{2}( \vec {PO} + \vec {OQ}) \)
\(= \vec {OP} + \frac{1}{2}( -\vec {OP} + \vec {OQ}) \)
\(= \frac{1}{2} (\vec {OP} + \vec {OQ}) \)