Given:

Maximum magnitude Rmax = a + b = 17 units

Minimum magnitude Rmin = a – b = 7 units

on solving these eqns, we get, a = 12 and b = 5

When the vectors are at right angle, the magnitude of the resultant vector will be

√[a^2 + b^2] = √[12^2 + 5^2] = √[169] = 13