a particle is subjected to two displacement as follows: 30m to the northeast and 40m to northwest. what must be third displacement if the particle is to end up at the starting point

Answer 1

notice the right triangle in the vector diagram. 3,4,5 triangle...so 50m is the displacement magnitude

Now for the angle.
sketch it.

I see at the bottom angle, the angle
arccos 30/50-PI/4, E of S. or 8.1 deg E of S

check that.

Answer 2

a particle is subjected to two displacement as follows: 30m to the northeast and 40m to northwest. what must be third displacement if the particle is to end up at the starting point