I'm not sure if my reply is really helpful for you because you should have some knowledge about vector geometry if you want to do this problem. Nevertheless here we go:

1. The man is described by the vector (Drawn in black).

2. The direction of the sunlight is described by .

3. The ray of sunlight which passes over the head of the man is described by the equation of the line l:

x,y,z)=(0,0,2)+t \cdot (-1,0,-1)" alt="lx,y,z)=(0,0,2)+t \cdot (-1,0,-1)" />

4. The equation of the plane p can be written as:

5. Now calculate

6. The point where the ray hits the plane - that means the point where the shadow of the man ends - is . So the length of the shadow is (Drawn in red)