Maxscript: This snippet demonstrates how to calculate the corner point for a right angle when knowing 2 points and a normal.

Finding Right Angle Point | .ms

fn GetVectorsAngle v1 v2 =
(
	theAngle = acos(dot (normalize v1) (normalize v2))
)

fn PlaceAlongVector pos:[0,0,0] vec:[0,0,1] offset:0 =
(
	pos + (normalize (vec)) * offset
)

/* Test Scene Setup */
clearlistener()
format "\n"
delete objects
pln = plane width:5 length:5 pos:[0,10,10] wirecolor:yellow
rotate pln (angleaxis 30 [1,0,0])
s1 = sphere pos:[0,30,0] wirecolor:red radius:2

center = pln.pos
normal = pln.transform.row3

/* Find the length to create a right traingle */
-- get angle difference between 2 vectors
difVector = s1.pos - pln.pos-- vector between plane and ball
objVector = pln.transform.row3 -- vector using normal of plane
dist = distance pln.pos s1.pos
calcAng = GetVectorsAngle difVector objVector

-- calculate the length of side to create a right angle
len = cos(calcAng) * dist
-- place point which would create a rightAngle at the sphere
cornerPos = PlaceAlongVector pos:pln.pos vec:objVector offset:len  
point pos:cornerPos size:2 wirecolor:yellow

I'd rather keep getting the point-line projection simple, i.e.

point pos:(pln.pos + pln.dir * dot (s1.pos - pln.pos) pln.dir)

where pln.dir is (obviously) a unit vector.