Adik-adik terkasih, hari ini kita mau belajar tentang vektor. Siapkan notes dan pensil kalian.. jangan lupa stabillo untuk menandai rumus-rumus pentingnya.. selamat belajar..
Kalian bisa juga pelajari latihan soal ini melalui chanel youtube ajar hitung. Kalian bisa langsung klik video link berikut ini:
1. Diketahui titik A(2, 7, 8); B(-1, 1, -1); C(0, 3, 2). Jika (AB) ⃗ wakil u ⃗ dan (BC) ⃗ wakil v ⃗ maka proyeksi orthogonal vektor u ⃗ dan v ⃗ adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVLNru1RSEQr7v1yqqyXge4blnpLB32kSa63Hav4FMQKD1UbCh0xIDud9UxW4VxzmDt6lNWUEpQpSZbVnxTxtQTFsFMHVYVJ6pv5LeoEUsCcQK2WxhPfDld2m6AXOrvMG7LjhaOYZxVks/s1600/a.png)
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBczbFKlhyHc3OS6DqT-UmMQvXVFF0T5b5xauCc8BLjUERdI0cNnEOtOdR7KKWTqb9-zF4uxRa4noo2goehvTGxnHztsUZ-gwLd7LLnHgEu5WrtSoWteMv8Bhh0HrU64RiDe7FSo8bKGE/s320/a.png)
Rumus untuk mencari proyeksi orthogonal vektor u ⃗ dan v ⃗ adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHQV8quPagWv6NLc_hbB_Bo5q-DkimGYpDkgZfZc-38SPVGC5djyDrg0nbvfImpz4TZnOVkPiThcki65k0gd3LYuRYwlILde0D9RXGCsixLgw-KOD4MNOhxNJrE3yewhWYUGd6dZiv4mo/s1600/a.png)
Mari, kita cuss kerjakan soalnya:
Proyeksi orthogonal vektor u ⃗ dan v ⃗ adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir5Iw4tQhZFaeoPTlq5_nwteeFOgSkGpz7eJN12mZ-ADL-CIowPRe1em9u-fIukZB3aNFzGKwaC6xfzQQJEaynmjoFsglW4jo8ysyE0U2O4JnhG98iNceZOwdylZa61Gubn3prYRZ-9kA/s1600/a.png)
JAWABAN: A
2. Diketahui vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRmz06ZKzdQMEQTx6A1rUqVV78jVpGzOeVlb4Srwm9gaNfLnJKH9uMuwpUFEy251TJ0le0ssDHomE2442nKsjMny9lwCUgdHwkVgoEZfs9Bllt5m_fSokYdwFrS0On7FxC-yvPBV411NI/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVbsDzSD4wm5WS-wvEdu5Wx7NVrArPqLnC5LbGuzncHmt6axM5X64U2whwLbiz8tK_kEeiTEmC1WokpvVCMYtTYCdV3xeOTtBV5lR1nYcDl48oDMSWmFgQigAoo6oSLUPMQe3KGLBnfHk/s1600/a.png)
a. 108
b. 17
c. 15
d. 6
e. 1
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCcXueHzLYpB18jkxi7tOL6xZBlHuNc897ELxvMGY70f4Jhz46OleRn1CGxj8Idb2SEBh6ck2DsnDcwTJ1WyXPvP0BbC-jaInsUeygiSZZhftj6248IYSGKujW8JrvhgEv5LIFgfBIkxU/s320/a.png)
(a – 6)(a – 1) = 0
a = 6 dan a = 1
- Untuk a = 6, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisGYGXn1MOmwiBkkkDqTiCvRod4imWFt53rMR6jjPr3I8KQNcKZGv68z1vcK-RQY51fkUbwB-IR6JIW4WtoXMlKQm_xw-QjaGbMDgJpdpq1buFAYglSObjOHB3vQICddIh6lvHinkps04/s1600/a.png)
- Untuk a = 1, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvjcuCshyOwh6jhRpCiWG3PC_baycHV8uLDAI7XFJ7mBTwUOFZPkyjiDur3OK5xHoJA6vddxJ8ZE1bc53W5LqrPUaemfboYE6HxBed2RkmCSsl5genaP7hTIj5vIgPWTQ7zsFJ153L_Ok/s1600/a.png)
Jadi, nilai maksimumnya adalah 17.
JAWABAN: B
3. Diketahui vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXr_FML9hIg9M29Z6zxnvY9ugxWyKkYhBzS1b95IJId3MSqa-Gv7lGMxfWFg2i3p_BPY8rjs1EDOOCxXx4AwFfMIXopR00FgUOggzV5ifh_i79fK27ivJzSam5KTRvAXdb3iPMWdUHWw8/s1600/a.png)
a. -1
b. 0
c. 1
d. 2
e. 3
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRP2Y5oX9cIgvWzm95smPlTceb4puYerbccDHS4IUUYf0PH2dNFMYg7wZBylheLb0_MXEjA0qiy02-sMqIuc_7rMrOulgxUP_nJOLfviAQGfvu-yli56-OjrXvz8vpYynTZxeR0wAk_cM/s320/a.png)
(a – 1)(a – 1) = 0
a = 1
JAWABAN: C
4. Diketahui vektor-vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhStpmqtj5VdqSGf_9v53lOnWDn7WgjkwVOFmI46sOxFGqYDiaDoJbpucF475s3kiCtlOc-WgBhmm2kkhoPtJ-yZhlm2HnSqZCzkYsO_AuyzoNf3EjB0NttRRy6wEXHzKGPFHRTkbszb6Q/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-s8FvV4SciWSGqaQMHpK3vqneXtGTlh-7iVLqjPmNcDrjxfinkm95NuCbE6alrXAxc15C1w5yi71hk3J7bSX9Bn2jH-nBy-BpZu_YUamC5r0TwbhJcQNnYzz2CJx94r7eEQ7jutpb5fQ/s1600/a.png)
PEMBAHASAN:
Soal ini dapat kita kerjakan dengan rumus perkalian skalar, misalnya vektor a dan vektor b, maka perkalian skalarnya:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPObgwf-uo19ZfF1b9pXBMSjicCfzYUmmFQd1FHl1Quqbg9qBtAiJkxQQjbc0ZqG0_8ElfZk3HPpbaDjEYt8V8EYh3AxBDufTJT2tHukKI-uB73annx0yRUGeP2_iBtS9NXuFsffndkCQ/s1600/a.png)
Misal, sudut antara u ⃗ dan v ⃗ adalah α, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqCGBqf0roVD4HLo3tQ_yiL4jvKK07v7DG00QT2LdaMBmh8EfmTSlEs2De-sNp5U8H9gRuJjhh0C004hfcF4ddTUBm3J08hAWS0ZaD3U3b8WB-6V6mx114fQ5W9Xe7G-cT61LOm8ceHWA/s1600/a.png)
JAWABAN: C
5.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFGDYkIpjHRfnrlsEzGqA6xoShGjv0Nas4wv6oy0cXokTrWAoirRw5MfuBIvXG44stZUcb0l0qt2jsGNvZNfE86qBVM5eqlO0il4pQc0XWNKqFflEbRs9KLYlkV9yhjrB8qkb2atK1bYA/s1600/a.png)
a. -20
b. -12
c. -10
d. -8
e. -1
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoIatzXzQUTji2LXinHcyn7xJkVCHxwVU4shgyqhDEmmfk0eWG3fWFbtSZp9Y5nknPLi8As9BfcnZmsQRiYYTTTbcKH6s3CW2CchbOa5pihRTeNuBoqO553WY_9z2w92eVK8DG9Eq2p1g/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOSR_mw7WeoSmlbRh_IbGueOp3pKGThBGEDGYxwPkKUAbPBZ9F8nRIRv2ROlFPjkbNWENPRlUxogpT-Zu_WgF6EiN8guhc0GK_NzR1dHmN6d_4Cxsob0nmllQ1F7Z5_JF3Dn4VXDm8IBQ/s320/a.png)
JAWABAN: A
6. Diketahui vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIzsJbHNUDxp8EPDRtpqhjl0oCM1I-tgJgjI3j7gOi6vPNfOn0ZMXYTsbYB-S55Edv5l_7VxLOrLFZbIuKF11H8PP0Xt05hIr2n43ZhAq0arbtiS2ezzv2Qn3aHeiUUnuRaPo0F80JYuo/s320/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWJV2bIH2BYePii4ShatGVopY19y7BHpZi_w7Q7LpUVs7eYYMhZAbmUYbNlXu0RzGT6EbgOlqS_7LtYz23FIdBXhxHdnB_oJgUFB5YmJ-2pX7rmBXFDvX3q8qIIXySsrLzRMSPMjJ4dYI/s1600/a.png)
PEMBAHASAN:
Rumus untuk mencari proyeksi orthogonal vektor a ⃗ dan b ⃗ adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3IM-2iBJjnTB7zqbkmMRcnBkozdMoqpvRRdaieXXYHyXpBX0bZcFiwy5fWF6dP75kWXug06MOHvWHsyyx11FhqW6UUFUiAQ-WIWMFtlaiBlxnpl6PxgFokYqpyVqW2jAI9JMWrtD0znI/s1600/a.png)
JAWABAN: B
7. Pada persegi panjang OACB, D adalah titik tengah OA dan P titik potong CD dengan diagonal AB.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJwuh_85wFZIJ0iXiCw9O-VKT2uoNatGRJ6QZcURQ6lRJZ_PKcu8pxL2gyTqnvJXA975zNDMzzmRxSi9em1p_dYUXr85eHTZk-0fxdcPyCt1aFzESdFyoLOBh9oW57TUJWgifvMyaKb2A/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAvMwraWLwcnqkRGvq7GJPLgyJ_6jJzvHbB4nt23b_hfeAKYaeZQ3KBq_NYLvLebQy1h_TmsRkqIVH1e9fpW9G78uSYDrLrLqHU5-VrZ40Z2jIwQMw3V2oSaonAHXvum0MeMGShgC1v5c/s1600/a.png)
PEMBAHASAN:
Perhatikan persegi panjang OABC berikut:
CP : DP = 2 : 1
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUlhTtPEG8eXYbnbpDbmgFh_uloskcAVCuuDhGRX89YN6YP30YaDn8zl7T1cGE53UKGcJTXmTqiXp18ihewq6uSsTwWTaqw8lIgw7pnK0uNEgm2VXGET-B8oN-wJMZ4mx-i7KKXFvlsr4/s1600/a.png)
JAWABAN: B
8.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmWWRPkYw1MnLlDYNAIG-kv9B6y_MEwAdZ1MC-bd1TMtW2y-FBucPVQMJ_79aH2Uq4YiYQxNHOrRQOe4jJdueUH2GNHS4aABLJCbfGHxLfER1cZBktckSg2Qgqs8X3hF4LeiALJlu0Bgc/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu1ePtJ0ZPFmRH1INsFlbcwXEep8nIKG6eqiOxSXZc9FUZUJ6TVqN_vzNh6o_uk6OiABkHLPk1K0FzAqlJAFprPAH12vIp-jUn9ejJI5vLI4-8USfO_U9V_GBqXmUt1fd5hlccFVjfQLM/s1600/a.png)
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirTn-XrRYZrxvNcDUtPy6a-H8-tkhC-fTGF_BAzCfjPY2jyRPE8gYX4rYY8rs2lQPwJduxY15cE_eopeV_xD-2BFush5tNYaEbRRKLVb-w-hGKJKnHHD7jMsqFI3yE8KxS8dA-R1Ebx_s/s320/a.png)
2(-3) + 4(m) + 1(2) = 0
-6 + 4m + 2 = 0
4m = 4
m = 1
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz4dUXlI3d8g_hxtoWSIgJbTOV369UfOZYWGWaJeMu8BNkav-zXIQMzTd3QuwJsxaU1QPiEKbSFoEP4uwJbzRK6Zk59Z4oBqhlXCrmjS8l6hsJpDiDVstKsHJgO8O0ulF2Y5JVzjLGNXw/s320/a.png)
JAWABAN: B
9. Diketahui titik P (2, 7, 8) dan Q(-1, 1, -1). Titik R membagi PQ di dalam dengan perbandingan 2 : 1 panjang (PR) ⃗ = ...
a. √4
b. √6
c. √12
d. √14
e. √56
PEMBAHASAN:
Kita gambarkan soal di atas dalam ilustrasi berikut:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR73TEIiLTxl35QCfRUYxSQagaup5CqklZMoLZdCSNLb-WFtByINkvzfVC7aEDEc98veY4Bkev0lCs1zfoogndV7T68uVXywgZmqCTVY8z7O7fJ0x00Z8TmPebtYAteKEZwlP7B6LLSzU/s1600/a.png)
Vektor R = ( 2 . vektor Q + 1 . vektor P ) : (2 + 1)
= (2 ( -1, 1, -1 ) + 1 ( 2, 7, 8 )) : 3
= (( -2, 2, -2 ) + ( 2, 7, 8 )) : 3
= ( 0, 9, 6 ) : 3
= (0, 3, 2)
Maka, (PR) ⃗ = (2 – 0, 7 – 3, 8 – 2)
= (2, 4, 6)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMuFCwxkfAeuu_gm2M6Fto0-Ez-OyMpOqLC8V23yjUci-NaD1uk_iGJPp21DMGPaE90frpmjhvdUlXbm53JGfRrZEHrpnGol5efQfN_Iy839oClRgfzNJCE7uzWWaGPwyL3svNhoERLD4/s1600/a.png)
JAWABAN: E
10. Agar kedua vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwng4NxQtgi6MA15Kch3uVB76k5GbnMo0ON2astLKKJ0eRD4xzMjKYni-jy-XuJlKbOk0-9lWA8zu3vAIxk_fDyy8D9e3FGXHc-U8Vo_jmpO8hXKU9DxancKWynVBP_Aj3poThPfZPPPo/s1600/a.png)
a. -5
b. -2
c. 3
d. 4
e. 6
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXuyABTr0Rac5rZICoCNumZomn1eae-8g1vtpac2EmsOnk5XkvJPMjuCKlr5kPf1TQB_ycOuuYwajeZFY_yP4X_XU1AhzKrczF75VBiqWEwPmcPET1sg22eiUhWWrhTsU0Wx09KgVVjvg/s1600/a.png)
(x, 4, 7) = k(6, y, 14)
(x, 4, 7) = (6k, yk, 14k)
x = 6k
4 = yk
7 = 14k
k = 7/14
k = ½
Karena k = ½, maka x = 6k = 6.1/2 = 3, dan
yk = 4
y.1/2 = 4
y = 4 : ½
y = 8
Maka nilai x – y = 3 – 8 = -5
JAWABAN: A
11. Diketahui titik A(1, -2, -8) dan titik B(3, -4, 0). Titik P terletak pada perpanjangan AB sehingga
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbHhciqaALJqX4J6extLgPeY1bKEQvZBaVAXFlzGSNn20lToFki-qGQ0MxpK3vtCb6Ch0yRko_Uw5e5OHXVtKtv9zUbzXQsDMmfWRwAZGBZfBNgn2EMG6oUpZAAemkJSGZ48SDYb9X7uk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhABrf64jtPh4Jnw0HVDdstY-oDgQRSVardusHQzJUIEsRczUq5mZTxLbLqXshqyfEflvdulWd8F3IIq8I8Ym9F98ikJCxqe4GinSst15TE0IcnOIoLTLMBXG03bJpYcGDkKwr3H-ujB-I/s1600/a.png)
PEMBAHASAN:
Mari kita ilustrasikan soal tersebut dalam gambar:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmFEIIJo_yXHmoL3RcPrWXvx4bxxxXhL0ApfbnWMkhJrjTzKJgkTJBwewshsofJBvbBYc-SscKaeHmarX-2Y_CU5tV3SWmz4TiUP5AfAUEX4dhQi9ILsLz0s3puO6eH9vMRR0MrYt678Q/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0mcknMxRc5-nLvsMkblCGSLStFT-6__Ql_BdFQP-0rCwFHAYitvmiaCuJpnquSGI0lBJ2DSueq82N2si8_yln3mtIv2cG6lPQQ0cB0TJ3mXmqYn-a8Qe-qjtZgTtmRrLbmGUeLCUDgFg/s1600/a.png)
JAWABAN: A
12. Jika besar sudut antara vektor p ⃗ dan vektor q ⃗ adalah 60 derajat, panjang p ⃗ dan q ⃗ masing-masing 10 dan 6, maka panjang vektor p ⃗ - q ⃗ = ...
a. 4
b. 9
c. 14
d. 2√17
e. 2√19
PEMBAHASAN:
Panjang vektor p ⃗ - q ⃗ adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgquWh041QJAPuc_H-JHBdMNMt2fv4WYz14Xi_yArrYPDKiSsf01L3Kqpra2HBvrRffhVGjmi1-a_1ZGiVsHA0JRbyZpU7Ls8iHnTa-5ihKEoqm6_FiSfYhYiJyXMa361AF_QcA69pjePM/s320/a.png)
JAWABAN: E
13.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs-EFIL8B876uknyi9XQDgx3ffXRspmPYGlES-tEZEoThbOUnZpBLaBC42Wr_McrygWln8QTjdPRingkLrtZEXb47g7jNeThOC14g4yVD19G8fZjnWsR9bZWyQHmA-heXx_mflUldlTbg/s1600/a.png)
a. 4
b. 2
c. 1
d. 0
e. -1
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiv06i6obzUX_0yg0aRbsIVjDPwNaE1eLyCpUg3nliFmSRZxZ3g2uDIGT8tJfDFMkowc9RILRrPUjgI24dGE9pT-f67nSUlVhsb5uvX6uJxodZw1cCJ4Uqti1ra-1YIL2lqcIR-1ZqnVvk/s320/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxOzFqO7xtBRVZHpBWYaVkRd0jnwIkKuZdIuNkJjSoyTMLmlI5hsr4Yc_3yCMnCLucjwKb_S3LXk1q9cakZqp1Ax7JvUFPNugQoa1SebgwBwYoR09GQOG8mUaFGUW9gYDcTT7ffPKk664/s1600/a.png)
JAWABAN: D
14. Agar vektor a = 2i + pj + k dan b = 3i + 2j + 4k saling tegak lurus, maka nilai p adalah...
a. 5
b. -5
c. -8
d. -9
e. -10
PEMBAHASAN:
Vektor a dan b saling tegak lurus, maka a . b = 0
a . b = 0
2(3) + p(2) + 1(4) = 0
6 + 2p + 4 = 0
2p = -10
p = -5
JAWABAN: B
15. Vektor yang merupakan proyeksi vektor (3, 1, -1) pada (2, 5, 1) adalah ...
a. 3/10 (2, 5, 1)
b. 3 (3, 1, -1)
c. 1/30 (2, 5, 1)
d. 1/3 (2, 5, 1)
e. 1/3 (2, 5, -1)
PEMBAHASAN:
Rumus untuk mencari proyeksi vektor a ⃗ dan b ⃗ adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFfzBtdqw_vjsl0BVUzLJvCCW24BorTAfLOELVQ58Ij4WzJy-vPu1kqipDVslfNki51Z5a18S2vAKpIW57f8z8g4c7oBBLG8rkfR-YTZ27fRj2hLOm5NaFTba2anr9CqNXo2j-gmnjxvM/s1600/a.png)
JAWABAN: D
16. Nilai p agar vektor pi + 2j – 6k dan 4i – 3j + k saling tegak lurus adalah ...
a. 6
b. 3
c. 1
d. -1
e. -6
PEMBAHASAN:
Agar saling tegak lurus maka hasil kali kedua vektor tersebut haruslah nol.
( pi + 2j – 6k ) . ( 4i – 3j + k ) = 0
p(4) + 2 (-3) + (-6)(1) = 0
4p – 6 – 6 = 0
4p – 12 = 0
4p = 12
p = 3
JAWABAN: B
17.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9F7JSR2Inn8N97Wd4KVvnlISgVeSZNpXZSfS4VijMYgy3cDosRNrZOF2obFyAjxJZuQhoqlC6mraSOLFt73OHwQjHorJ0qSQnULA3lqpUVPJT6wa_z38YQoHtevs0z2-kVeCxmXzfZcE/s1600/a.png)
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeDhR6LwkTI9Ek9-3mK9r1PcUN67yqm_yfs1n9tZ4soKRUYi_4ApNyYIKAw0JT51gI_ikyQmUCr2BmsHKzJ2n6ELg7CtAKcyHK5gkW7wzWoh8WHfw9Hxd6jZE13FKLRyCn_G-i88DYL94/s320/a.png)
JAWABAN: D
18. Diketahui titik A (5, 1, 3); B (2, -1, -1) dan C (4, 2, -4). Besar <ABC adalah ...
a. π
b. π/2
c. π/3
d. π/6
e. 0
PEMBAHASAN:
(AB) ̅ = (2 – 5, -1 – 1, -1 – 3) = (-3, -2, -4)
(CB) ̅ = (2 – 4, -1 – 2, -1 – (-4)) = (-2, -3, 3)
Besar <ABC adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIHFrw7O-xK70hNfY0OikmkB5E2O53ZRi31t4SLM09wZXH-ueHrs8N6CL1doa7WkJ8I4TMvsH6mKvG2nhH9Pc9pQ2pSRz5vkoaeB6AIZ0lbV7pFStBeJp6YNrEu648_lWaSr4B5TmvIZg/s1600/a.png)
JAWABAN: B
19. Diketahui vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2PeEr56tpcSilDTIU6sAw6qh89cNy1Quxp7VHbiEUKdqWGpxhfGkRkDnvIg0xO-t_1QgbhmcdS5MJIPJ-7jWL20ynRUeP1gMHanY-MkxZPb_LdmnV8QUhVC_sII2PGRpento890aKKpk/s320/a.png)
a. -1
b. -1/3
c. 1/3
d. 1
e. 3
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7GZHk6tHqqkI76zAfi549X9lM2KCkf66QgNkwVSbRml1I-0xP5dduhNhoDBFyWWxRJP9Rw71DNiDI-1bxNB-QOTT7ftowZKuF1KC_mUl9M__SyVii6UozyGNc1DsP9ueWAfRKmB4PFhk/s320/a.png)
(6 – 3a)3 + (4 – 9a) 9 + (-2 + 12a)(-12) = 0
(18 – 9a) + (36 – 81a) + (24 – 144a) = 0
18 + 36 + 24 -9a – 81a – 144a = 0
78 – 234a = 0
234a = 78
a = 78/234
a = 1/3
JAWABAN: C
20. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnq-dM6B6E3nNM7J78wMfCFj-TeM-Z9TfttIryEymEHwhXhVsI1WXqINlaAgiKDzaTyUCIJenvqQbSxGEKXtuyuM1PMZwasRfAOmczNBLDbKHoi_z0knHz5plvarWhA63V325TMNQN9po/s1600/a.png)
a. 3/5
b. ¾
c. 4/3
d. 9/16
e. 16/9
PEMBAHASAN:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic5iyYFmZr3A6RI1M11khY8DSJo6_tkXsUTIm48kEO1Yc5ybXUxOFNOiT4_HMseEQbEdoVs2MaESq1LPHrOzBW5fq6mNruuYq-O2EVvRBkUGFjmexvBEzVhrCdi2SP8WHlfdCKgHSqSDI/s1600/a.png)
tan θ = 3/4 , ingat segitiga siku-siku
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO6uMTI6T0c41djo0YlkCZIQtPhveUHFhuOIhVAQYViWXfhIf3rylf3KcE31drAYSnjwMhNpXaVYpu74fK6h7Es1oyWreyhdIs1h8xY1ybPZ2VcQ74KXJJ-qVjI2Lu-QdcDiHP8rokSxA/s1600/a.png)
JAWABAN: B
Menyenangkan kan latihan kita hari ini? Sampai ketemu dibahasan soal selanjutnya..
Makasih banyak, padahal sebelumnya saya benci bab ini wkwk
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