Given that P = (5 , 1) and Q = (13 , 8)
The component form is
Vector PQ = Q - P
Vector PQ = < 13 - 5 , 8 - 1 >
Vector PQ = < 8 , 7 >
The magnitude vector is obtained by formula
| < x , y > | = sqrt (x^2 + y^2)
| < x , y > | = sqrt (8^2 + 7^2)
| < x , y > | = sqrt (113)
| < x , y > | = 10.63
Therefore the component vector is < 8 , 7 > and magnitude of the vector is 10.63.