Page 232 - Math Grade 11 (Advance)

PROEUS DARA

(II' 0
2 fl'ltnt nn Q iHlitfl Lli nm tn tiH'ilJ ru
1 1
HH'irul~ihru co.~. j, k) tr:i21ti~ (a) fr:Hl5Yl2
u ~~
~ ~ 0
M'i:H1U ax+ by+ cz + d = 0 Sburulu
1
y
P (x , y , z ) Y2ts4Qh1J~ (a) '1
0
0
0
0
1
mh H ctlGtNTHlifnh ~s P 0 tilly~ (a) '1
X
Llif1h P H tUTlrhu~runGN]u P 0 wi
0
y~ (a) '1 ~nu~ru d(Po, a) riGNJu Po wiy~ (a) '1

2 2 2
P P = 1&1 = Ja +b +c '1
1
0
mh (xH, YH· ZH) ctl~HHtlltStS H tS'Utf3iQ1S P;H. YlS~HHtllt2
(xH-xo, YH-Yo· zH-zo) tS'H
----7 ---7 7 ---7

P P ·P H = u·P H = a(xH-x )+b(yH-y )+c(zH-z )
0
0
0
0
1
0
0
= (axH + byH + czH)- (ax + by + cz 0 )
0
0
ttnru HE(a) tr:itflS (axH+byH+czH) = 0 2h ax +by +cz = -d
0
0
0
----7 ---7
(P P • P H) = -(ax + by + cz ) (1)
0
1
0
0
0
0
P7t · P;H. = IP:ltll?oHicose (2)
~ 1---71 -(ax 0 + by 0 + cz 0 +d)
P P ·cos
m'tl ( 1) sh (2) tr:iffl mms P 0 H = P 0 H = I I
~ 0 1 8

lax 0 + by 0 + cz 0 + dl
(
)
d = p o' a = p oH = '1
J 2 2 2
a +b +c
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