-
ใใฎ
ๅบๆฌ ไพ้ก 13
ใชใ่งใใใใฏใใซใๆฑใใ
B, ACOR
(1)
ๆญฃใฎๆฐใจใ, ใใฏใใซ = (1,1)
2.29 ๅบๆฌไบ้
2
00000]
(1) ใใใใจใใใใ
ใพใใจใฎใชใ่งใ60ยฐใฎใจใใฎๅคใๆฑใใใ
[(1) ็ซๆๅคง]
(2)=(1,2)=(m,n)(mใจnใฏๆญฃใฎๆฐ)ใซใคใใฆ ||=โ10 ใงใใ,
33
1็ซ
ใจใฎใชใ่งใฏ135ยฐใงใใใ ใใฎใจใ,m, nใฎๅคใๆฑใใใ
ๅบๆฌ12
3
ใใ
CHART & SOLUTION
ใชใ่งใใใใฏใใซใๆฑใใ = (a1, a2), = (b1, bz)ใจใใใ
ๅ
็ฉใat=a||| cose, at=ab+azb2ใฎ2้ใใง่กจใ
ๅ
็ฉใ2้ใใฎๆนๆณใง่กจใ, ใใใใ็ญใใใจใใใๆน็จๅผใ่งฃใใฐใใใ
(1) ใฏ (2) ใงใฏm, nใๆญฃใฎๆฐใงใใใใจใซๆณจๆใใใ
โ ) ใ่งฃใ ๅ
่งฃ็ญ
0ยฐ
1x
60ยฐ
1
1x
ๆฑใใ
ใจ
(1)=1ร1+1x(-p)=1-p
|a|=โ12+1?=โ2,16|=โ12+(-b)=โ1+12
โๆๅใซใใ่กจ็พใ
a = |a|||cos60ยฐใใ 1-p=โ2โ1+x
โ
ๅฎ็พฉใซใใ่กจ็พใ
201
โ ใฎไธก่พบใ2ไนใใฆๆด็ใใใจ
ใใฃใฆ p=2ยฑโ3
p2-4p+1=0
(1)=1/12(12)
ใใใง,โ ใใ, 1p0 ใงใใใใ 0<p< 1
ใใใซ p=2-โโ3
ๆด็ใใ
1+0 ใงใใใใ,
โ ใฎๅณ่พบใฏๆญฃใ ใใฃใฆ,
โ ใฎๅทฆ่พบใๆญฃใงใใ,
1-p>0
(2)|5|=โ10ใใ ||=10
ใใฃใฆ mยฒ+n2=10
......
โ
||=โ12+(-2)ยฒ=โ5 ใงใใใใ
aโข6=|a||6|cos 135ยฐ=โ/5 รโ10ร(-1/2)=-5
COS
ใพใ, a1=1xm+(-2)xn=m-2n ใงใใใใ
m-2n=-5
ๅฎ็พฉใซใใ่กจ็พใใ
ใใฏใใซใฎๅ
็ฉ
โๆๅใซใใ่กจ็พใ
ใใใซ
m=2n-5..... โก
โกโ ใซไปฃๅ
ฅใใใจ
(2n-5)2+n2=10
ๆด็ใใใจ 5n2-20n+15=0
ใใฃใฆ
ใใฃใฆ
n2-4n+3=0 ใใใซ
n=1,3
โกใใn=1ใฎใจใ
m=-3, n=3 ใฎใจใ m=1
(n-1)(n-3)=0
m, n ใฏๆญฃใฎๆฐใงใใใใ
PRACTICE
13ยฐ
โm=-3<0 ใใไธ้ฉใ
m=1, n=3
\)\)= 20
(1) OA = (x, 1), OB=(2,1) ใซใคใใฆ, OA, OB ใฎใชใ่งใ45ยฐใงใใใจใ, xใฎ
ๅคใๆฑใใใ
(2)=(2-1) = (m,n) ใซใคใใฆ,16=2โ5ใงใใ,ใใจใฎใชใ่งใฏ60ยฐใง
ใใใใใฎใจใ,m, nใฎๅคใๆฑใใใ