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