Gpi cp la goc giua A va (P), ta c6:
sin9 = —. a + 2b + 2c
" A
5a + 6b
3Va2+b2+c2 3V5a2+8ab + 5b2
Nell b = 0, taco sin(p = s
Neu b ^ i O ^ t a c o : sincp = -
3 \
25â + 60ab + 36b^ _ 1^ 25t^ +60t + 36 _ a Sâ+Sab + Sb^ 3 ^ St^+St + S ' " b Xet ham so f ( t ) . ^gj:^0t + 36 ^ ^ , ^ -lOOt^ - l l O t . 12
5 t ^ + 8 t + 5 Suy ra f'(t) = O o t = — , t = - - 10 5 (5t^ +8t + 5)' l i m f(t) = 5, f t->±oo 10 = 0.
Ta CO (p Ion nhat <=> sincp Ion nhat <=> f(t) Ion nhat « * = ^
00
Cty TNHH MTV DWH Khang Vict
Hay - = — , ta chon a = 1, b = 10, c = 22. b 10
Phuong trinh (p): x + lOy + 22z + 41 = 0 . Cach 2: Giai bang p h u o n g phap hinh hcac
Goi d la d u o n g thang d i qua M , song song v o i A . Ta c6: N M = ( 2 ; 2 ; - l ) x = l + 2t
Suy ra p h u o n g trinh d : ' y = 2 + 2t, tê z = l - t
^ \ Tren d ta lay diem B(3;4;0).
Goi H , K Ian lugt la hinh chieu cua A len (P) va M N , k h i do ((a),A) = B M H .
„ , M H ^ M K Ta co: cos B M H = --—->——•,
M B M B
ma khong doi nen B M H Ion nhát <=> H = K M B ^
Hay (P) la mat phang d i qua M N va vuong goc v o i mat phang (y) = ( M N , d )
Taco: = N M A i l ^ = (6;-5; 2) . Suy ra i ^ = N M A r ^ = ( - l ; - 1 0 ; - 2 2 )
Vay p h u o n g trinh (p): x + lOy + 22z + 41 = 0 .
Ca BAI TAP
Bai 3.5.1. Trong khong gian cho ba diem A ( l ; 2 ; 3 ) , B ( - l ; 0 ; - 3 ) , C ( 2 ; - 3 ; - l ) 1) T i m M thuoc mat phang ( a ) : 2 x + y - 2 z - l = 0 sao cho bieu thuc sau nho nhat S = 3 M A ^ + 4MB^ - 6 M C ^ ,
2) T i m M thuoc d u o n g thang A : ^ = ^ = ~ - sao cho bieu thuc sau Ion nhat: P: M A - 7 M B + SMC