First we establish the coordinates of all relevant points where A is <0,0,0>.
B=<4,0,0>, C=<4,4,0>, D=<0,4,0>.
Starting vector of the moth M=<0,0,1.5>.
Light bulb vector L=<2,2,2.5>.
Destination E=<2,4,3>.
The path of the moth is ML, LC, CE. These are displacement vectors.
(a)
AM+ML=AL, ML=AL-AM=<2,2,2.5>-<0,0,1.5>=<2,2,1>
AL+LC=AC, LC=AC-AL=<4,4,0>-<2,2,2.5>=<2,2,-2.5>
AC+CE=AE, CE=AE-AC=<2,4,3>-<4,4,0>=<-2,0,3>
AE is the position vector of the moth at its destination=<2,4,3>.
The 3D representation is shown below and is best viewed using 3D lenses (red filter left and blue/green filter right).
The point K<2,2,3> is where the light bulb is attached to the ceiling NFGH.
(b) The magnitudes of the displacement vectors are the distances between their endpoints.
|ML|=√(22+22+1)=√9=3m;
|LC|=√(22+22+(-2.5)2)=√14.25=3.7749m approx;
|CE|=√((-2)2+0+32)=√13=3.6056m approx.
Total distance = 3+3.7749+3.6056=10.38m approx.
(c) |AE|=√(22+42+32)=√29=5.3852m (5.39m) approx.
More to follow...