Page 215 - Math Grade 11 (Advance)

PROEUS DARA

z

---71 I 2 2 2
PQ = 1 PQ = ~~j(Xz-xl) +(yz-YI) +(Zz-zl) y

tl m s g u'tfl rm n tJ P El tJ Q R n.n ~
u .,

X

0 • 0
rutrrH'il'!U
IJ
n. Q(l, 2, 3) , P(3, 4, 5) 2. A(-1, -2, -5) , B(-3, -4, -5)

0
""'
n. run d dlu'tflru~ntlmun.nu Q(I, 2, 3) , P(3, 4, 5) tSlHt:iOIS
., 1
2 2 2
d = (Q, P) = PQ = J(3-1) +(4-2) +(5-3) = J4+4+4
= Jl2 = 2/3 '1

2 2 2
2. d(A, B)= AB = J(-3+1) +(-4+2) +(-5+5) = J4+4+0
= J8 = 2J2 '1

II J ~ ~ 7 0
ntlni'tlli5HHiM~'tflrn (0; i, j, k) tt:i'tflSullilu M(3, 1, 5) , N(3, 5, 1)
~ ~ U I
1 I
stJ P(-1, 5, 5) '1

2
6'il'tll51Yltl tt:iOIS MN = J(3-3) +(5-I) +(1-5) = J32
2
2
MP = J(-1-3) +(5-1) +(5-5) = J32
2
2
2
--7 "" ---7
n:ilru MN = (0, 4, -4) Stl MP = (-4, 4, 0) tmgt?JOIS
--7 ---7
MN·MP = (0)(-4)+4x4+(-4)(0) = 16
--7 ---7
cosS = MN · MP = 16 = 16 = ! =:> 8 = ~ '1
1~1-IM?I J32 X J32 32 2 3

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