Page 235 - Math Grade 11 (Advance)

PROEUS DARA

-? -? -? -? -? 7 7 7 -? 7
(1). a+b = b+a (2). (a+b)+c = a+(b+c)
7 -? 7
(3). (mn)b = m(nb) ( 4) . ( m + n )a = ma + nb
-? 7 -? -?
(5). m(a+b) = ma+nb

ttl mb = 0 &S18&?1Q12 m = 0 'li b = 0 '1
.....
- n. tti P(x, y, z) sb P'(x', y', z') ctlrJjf3bl.fjtlt2bthflL'lintitthliH1L'i:Hi5
1
7 7 7
(0, i, j, k) t?1Q12
• P = P' hl'I§1Hli x = x' S b y = y' 2 b z = z' '1
u
Gl p "' P' hl'l§'i§ ru X "' x' 'li y "' y' 'li z "' z' '1
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.....
u
--7
e P'P 'i:f12~HHt:iH2 (x-x', y-y', z-z') '1
• 13Mtlnn.mru~s PP' 'i:f12FiHHtht2 (x+x' y+y' z+z') '1
1 n u 2'2'2
2. ttl~= (x, y, z) sb ~· = (x', y', z') ctlrJj1{jgjfihrth . .fl'i'UFititthli.Hfnru
I ct l._j
1
7 ~ 7
(i, j, k) t?1Q12
• t = t• <=> x = x' , y = y' , z = z' '1

• h "' t• <=> x "' x' , y "' y' , z "' z' '1

• 1tlfli (t-h') 'i:f12FiHHtht2 (x-x', y-y', z-z') '1
l u
• \fkEffi 1tlfla kt 'i:f12FiHHtht2 (kx, ky, kz) '1
1 u

(kx + k'x', ky + k'y', kz + k'z') '1

dru?lrulhlltru~SrJj1tlfli h Sb t Fibrthn ~ctlf3SStln k 'l§li5
1 n 1 "' u u
1
7 7
7 7 ""7 7
.. k = u . v = 0 t'li u = 0 'li v = 0 '1
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