Q1: At a given instant ship A is travelling at 6 km/h due east and ship B is travelling at 8 km/h due north. The velocity of B relative to A is

ANS:D - 10 km/hrs

Don't get confused between resultant and relative velocity they are completely different (although in this particular case, the value is the same). The result can be easily determined from vector operation.

Here, Va = 6i + 0j and Vb = 0i + 8j, Thus Vba = Vb - Va = -6i + 8j,
Hence Magnitude of Vba = Sqrt (6^2 + 8^2) = 10 kmph. Efx = 6.
Efy = 8.

Resultant R= {sqr(Efx)+sqr(Efy)}1/2.
R = (36+64)'1/2.
R = (100)'1/2 = 10.