Maxscript: This snippet demonstrates how to rotate a node around a given vector, 'X' degrees. This example rotates a sphere so it aligns with another objects vector based on the same origin.

Rotate Node Around Vector X Degrees | .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
)

fn GetRightTrianglePoint posA:[0,0,0] posB:[0,0,0] =
(
	/* Find the length to create a right traingle */
	-- get angle difference between 2 vectors
	difVector = posA - posB-- vector between plane and ball
	objVector = pln.transform.row3 -- vector using normal of plane
	dist = distance posB posA
	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:posB vec:objVector offset:len
	cornerPos
)

/* Test Scene Setup */
clearlistener()
format "\n"
delete objects
pln = plane width:5 length:5 pos:[0,10,10] wirecolor:red; rotate pln (angleaxis 30 [1,0,0])
ballA = sphere pos:[15,35,0] wirecolor:blue radius:2
ballB = sphere pos:[32,18,7] wirecolor:green radius:1
/* END Scene Setup */


-- calcualte corner positions along axis of rotation
ballApt = GetRightTrianglePoint posA:ballA.pos posB:pln.pos
point pos:p1 size:2 wirecolor:blue
ballBpt = GetRightTrianglePoint posA:ballB.pos posB:pln.pos
point pos:p2 size:2 wirecolor:(random yellow green)

-- now calcualte the angle need to rotate the blue ball so it aligns to the red
vectorA = p1 - ballA.pos
vectorB = p2 - ballB.pos
ang = GetVectorsAngle vectorA vectorB
-- crs = cross vectorA vectorB

/* Mohamed METHOD */
-- Step 1 - the point to rotate around
pt = pln.pos
-- Step 2 - the vector axis to rotate around
vectorAxis = normalize (pln.pos - ballApt)
-- Step 3 - getting input matrix
inputMatrix = ballA.transform
-- Step 4 - to rotate around another point P, you need to translate(-P) , then rotate(r) , then translate(P)
-- you have a vector to rotate around, and an angle, (v, a)
translate inputMatrix -pt
rotate inputMatrix (quat ang vectorAxis)
translate inputMatrix pt

-- Step 5- now apply this matrix
resultMatrix = inputMatrix
sphere transform:resultMatrix wirecolor:black radius:2