10. 已知空間中兩點A(4,3,2)、B(2,1,4),P點為平面E:x-2y-2z=1上的一點,則
PA' + PB²的最小值為 (10-1) (10-2)
14
XP(x, y, z)
PA³ = (x-4) + (y-3) + (3-2)²
ƒ³| A £√15 (x-4)+ (y-3)+ (8-2)² ] [ (+ (-2)+ (-2)³]
11 PA³ ¾ 25-5
9
PB²= (x-2)+ (y-1)²+ (8-4) *
2 2
> (X-4-24+6-28+4)=5
2
2
[(x-2)² + (y-1)² + (8-4)²] ( 1²+ (-2)²+ (-2)²) >( X-2-24 +2-28+8)= 1
11 PB² = 49
2
" PA + PB² = 14
9