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Soal Vektor UMBPTN, help!

Dimulai oleh nash, Juni 14, 2009, 08:05:39 AM

« sebelumnya - berikutnya »

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nash

soal UMB PTN 2009, MAT.IPA kode soal 120
no.5

Jika vektor a dan b memenuhi (a + b) dot b = 12, |a| = 2, dan |b| = 3, maka sudut antara vektor a dan vektor b adalah...

ni soal sisa yg aku ga bisa,
mohon bantuannya ya!
"Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart"

(John Nash, "A Beautiful Mind")

Mtk Kerajaan Mataram

(a + b) dot b = 12 ==> a dot b + |b|^2 =12 karena |b| diketahui maka kita peroleh nilai dari a dot b. Dan selanjutnya adalah
cos(sudut antara a dan b) = a dot b / |a||b|.

nash

sejauh ini, bgnilah caraku:

(a+b) dot b = 12
<=> |a+b|.|b|.cos A = 12
<=> |a+b|.3.cos A = 12
<=> |a+b|.cos A = 4
kdua ruas dkuadratkan:
|a+b|^2.(cos A)^2 = 16

smtara itu:
|a+b|^2 = |a|^2 + 2.a dot b + |b|^2
<=> |a+b|^2 = 4 + 2(|a|.|b|.cos A) + 9
<=> |a+b|^2 = 13 + 2(6.cos A)
<=> |a+b|^2 = 13 + 12.cos A

kalo dsubstitusikan:
(13 + 12.cos A)(cos A)^2 = 16
<=> 12(cos A)^3 + 13(cos A)^2 - 16 = 0

aku stuck di sini.
caraku salah ga?
"Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart"

(John Nash, "A Beautiful Mind")

nash

owh smtara ku nulis jwbn, om mataram reply

a dot b = 3
brarti
cos A = a dot b/|a||b|
= 3/6 = 1/2
berarti A = 60 drjat!


sesimpel itukah?
"Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart"

(John Nash, "A Beautiful Mind")

utusan langit

wah, kayaknya si nash minta yang rumit nich,.. wkwkwkwk

Mtk Kerajaan Mataram

@nash
Anda mengalami kesalahan di sudut :
|a+b|.|b|.cos A = 12
dan
|a+b|^2 = 4 + 2(|a|.|b|.cos A) + 9

Seharusnya berbeda, yakni misal :

|a+b|.|b|.cos A = 12
dan
|a+b|^2 = 4 + 2(|a|.|b|.cos B) + 9

sudut A = sudut antara vektor  \vec{a}+\vec{b} dengan vektor \vec{b},
sudut B = sudut antara vektor  \vec{a} dengan vektor \vec{b}.

nash

owh, ngerti aku.
makasih ya om

+1 IQ deh
"Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart"

(John Nash, "A Beautiful Mind")