QUESTIONS - ANSWERS - VECTORS - 3D GEOMETRY

QUESTIONS - ANSWERS - VECTORS - 3D GEOMETRY
Find the point P on the plane 0x+1y-3z=8 closest to the point Q(2,-3,3).
P = ( , , )?????(p,q,r) say
it on plane.hence
q-3r=8...............1
PQ is perpenicular to plane...or parallel to its normal
drs of plane = (0,1,-3)
drs of PQ = [p-2,q+3,r-3]
(p-2)/0 = (q+3)/1 = (r-3)/-3
p=2
r-3 = -3(q+3)=-3q-9
3q+r=-6..............2
3*eqn.1-en.2
-10r=30
r=-3
3q=-3
q=-1
hence p is (2,-1,-3)