·
التمرين الأول:(5ن)
(1ن) 1) - حدد جميع
قواسم العدد
34
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaaIZaGaaGinaaaa@3E1F@
.
(2ن) 2) - حدد جميع الأعداد
x
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG4baaaa@3DA1@
و
y
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG5baaaa@3DA2@
من
ℕ
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacqWIvesPaaa@3E10@
التي
تحقق:
(
x+1
)(
y+2
)=34
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaqadaqaaiaadIhacqGHRaWkcaaIXaaacaGLOaGa
ayzkaaWaaeWaaeaacaWG5bGaey4kaSIaaGOmaaGaayjkaiaawMcaai
abg2da9iaaiodacaaI0aaaaa@476D@
.
(2ن) 3) -
استنتج جميع الأعداد
x
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG4baaaa@3DA1@
و
y
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG5baaaa@3DA2@
من
ℕ
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacqWIvesPaaa@3E10@
التي تحقق:
xy+2x+y=32
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG4bGaamyEaiabgUcaRiaaikdacaWG4bGaey4k
aSIaamyEaiabg2da9iaaiodacaaIYaaaaa@4599@
.
التمرين الثاني:(4ن)
نعتبر العدد الحقيقي
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbaaaa@3D6A@
بحيث:
A=
3−2
2
−
3+2
2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbGaeyypa0ZaaOaaaeaacaWLa8UaaG4maiab
gkHiTiaaikdadaGcaaqaaiaaikdaaSqabaaabeaakiabgkHiTmaaka
aabaGaaG4maiabgUcaRiaaikdadaGcaaqaaiaaikdaaSqabaaabeaa
aaa@477E@
.
(1ن) 1) -أ- تحقق من أن:
3−2
2
>0
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbmqadeWacmGadiqabeqadmWabmabdaGcbaGaaG4maiabgk
HiTiaaikdadaGcaaqaaiaaikdaaSqabaGccqGH+aGpcaaIWaaaaa@3B17@
.
(1ن) ب- حدد
إشارة العدد الحقيقي
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
fr=xb9adbmqadeWacmGadiqabeqadmWabmabdaGcbaGaamyqaaaa@36D4@
.
(1ن) 2)
-أ- أحسب ثم بسط العدد الحقيقي
A
2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbWaaWbaaSqabeaacaaIYaaaaaaa@3E53@
.
(1ن) ب- استنتج
قيمة مبسطة للعدد الحقيقي
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbaaaa@3D6A@
.
·
التمرين الثالث:(6ن)
ليكن
x
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG4baaaa@3DA1@
عنصرا من المجال
]
1
2
,1 [
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaqcJaqaamaalaaabaGaaGymaaqaaiaaikdaaaGa
aiilaiaaigdaaiaaw2facaGLBbaaaaa@41AE@
، نضع :
A=
2x
x+2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbGaeyypa0ZaaSaaaeaacaaIYaGaamiEaaqa
aiaadIhacqGHRaWkcaaIYaaaaaaa@42D4@
.
(1ن) 1) -أ- حدد تأطيرا للعدد
x+2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWG4bGaey4kaSIaaGOmaaaa@3F3F@
.
(1ن) ب- استنتج تأطيرا للعدد
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbaaaa@3D6A@
محددا سعته.
(1ن) 2) -أ- تحقق من أن :
A=2−
4
x+2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbGaeyypa0JaaGOmaiabgkHiTmaalaaabaGa
aGinaaqaaiaadIhacqGHRaWkcaaIYaaaaaaa@4382@
.
(1ن) ب- استنتج تأطيرا آخر للعدد
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbaaaa@3D6A@
سعته
4
15
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWcaaqaaiaaisdaaeaacaaIXaGaaGynaaaaaaa@3EEC@
.
(2ن) 3) - بين أن العدد
2
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaaIYaaaaa@3D60@
قيمة مقربة للعدد
A
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbaaaa@3D6A@
بالدقة
8
5
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWcaaqaaiaaiIdaaeaacaaI1aaaaaaa@3E35@
.
·
التمرين الرابع:(5ن)
ليكن
ABC
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGbbGaamOqaiaadoeaaaa@3EF9@
مثلثا.نعتبر النقط
I
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGjbaaaa@3D72@
و
J
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGkbaaaa@3D73@
و
K
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGlbaaaa@3D74@
بحيث:
AI
→
=
1
3
AC
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGjbaacaGLxdcacqGH9aqp
daWcaaqaaiaaigdaaeaacaaIZaaaamaaFiaabaGaamyqaiaadoeaai
aawEniaaaa@45BC@
و
BJ
→
+
BC
→
=
0
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadkeacaWGkbaacaGLxdcacqGHRaWk
daWhcaqaaiaadkeacaWGdbaacaGLxdcacqGH9aqpdaWhcaqaaiaaic
daaiaawEniaaaa@4787@
و
AK
→
=−
AB
→
+
AC
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGlbaacaGLxdcacqGH9aqp
cqGHsisldaWhcaqaaiaadgeacaWGcbaacaGLxdcacqGHRaWkdaWhca
qaaiaadgeacaWGdbaacaGLxdcaaaa@4946@
.
(1ن) 1) - أنشئ شكلا مناسبا.
(1ن) 2) -أ- أكتب المتجهة
AJ
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGkbaacaGLxdcaaaa@3FED@
بدلالة المتجهتين
AB
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGcbaacaGLxdcaaaa@3FE5@
و
AC
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGdbaacaGLxdcaaaa@3FE6@
.
(1ن)
ب-
استنتج أن :
IJ
→
=2
AB
→
−
4
3
AC
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadMeacaWGkbaacaGLxdcacqGH9aqp
caaIYaWaa8HaaeaacaWGbbGaamOqaaGaay51GaGaeyOeI0YaaSaaae
aacaaI0aaabaGaaG4maaaadaWhcaqaaiaadgeacaWGdbaacaGLxdca
aaa@4AB2@
.
(1ن) 3) -أ- أكتب المتجهة
IK
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadMeacaWGlbaacaGLxdcaaaa@3FF6@
بدلالة المتجهتين
AB
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGcbaacaGLxdcaaaa@3FE5@
و
AC
→
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaadaWhcaqaaiaadgeacaWGdbaacaGLxdcaaaa@3FE6@
.
(1ن) ب- استنتج أن النقط
I
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGjbaaaa@3D72@
و
J
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGkbaaaa@3D73@
و
K
MathType@MTEF@5@5@+=
feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D
aerbufgAV1wyaebbfv3ySLgzGueE0jxyaibaieYlNi=xH8yiVC0xbb
L8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbbG8FasPYRqj0=yi0dXd
bba9pGe9xq=JbbG8A8frFve9Fve9Ff0dmeWabmqadiWacmGabeWabm
WadqWafmaakeaacaWGlbaaaa@3D74@
مستقيمية.
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