Doubt regarding intensity received at a point

I came across a problem which is as follows:

Screen S is illuminated by two point sources A and B. Another source C sends a parallel beam of light towards point P on the screen (see figure). Line AP is normal to the screen and the lines AP, BP and CP are in one plane. The radiant powers of sources A and B are 90 W and 180 W respectively. The beam from C is of intensity 20 W/m2. Calculate intensity at P on the screen.
( AP= 3 meter, BP=CP=1.5 meter)

So as the sources of light are different, we would not consider any interference and would just add the intensities. I am not asking you to solve the problem but had the doubt if only the intensities perpendicular to surfaces are the one visible? And if this is the case, why don’t we consider component of resultant intensity perpendicular to surface in case of young’s double slit interference pattern ?