The component vectors of P and Q are
OP = x1i + y1j + z1k and OQ = x2i + y2j + z2k
i . e ., P1 P2 = ( x2i + y2j + z2k ) – ( x1i + y1j + z1k ) = ( x2 – x1 ) i + ( y2 – y1 ) j + ( z2 – z1 ) k
Its magnitude is
P1 P2 = √ ( x2 – x1 ) 2 + ( y2 – y1 ) 2 + ( z2 – z1 ) 2
Position Vector of a Point
The position vector of a point P with respect to a fixed point , say O , is the vector OP . The fixed point is called the origin .
Let PQ be any vector . We have PQ = PO + OQ = — OP + OQ = OQ — OP = Position vector of Q — Position vector of P .
i . e ., PQ = PV of Q — PV of P