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Diketahui vektor u dan v di R 2 ​ . b. Jika ∣ ∣ ​ u ∣ ∣ ​ = 4 , ∣ ∣ ​ v ∣ ∣ ​ = 3 , dan ∣ ∣ ​ u − v ∣ ∣ ​ = 37 ​ . Tentukanlah ∣ ∣ ​ u + v ∣ ∣ ​ .

Diketahui vektor  di .

b. Jika . Tentukanlah .

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S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

.

 vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line equals square root of 85.

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Pembahasan

Ingat bentuk . Sehingga didapat: Jadi, .

Ingat bentuk  left parenthesis a plus b right parenthesis squared equals left parenthesis a minus b right parenthesis squared plus 4 a b.

Sehingga didapat:

vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals vertical line u with rightwards arrow on top minus v with rightwards arrow on top vertical line squared plus 4 vertical line u with rightwards arrow on top vertical line vertical line v with rightwards arrow on top vertical line vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals open parentheses square root of 37 close parentheses squared plus 4 left parenthesis 4 right parenthesis left parenthesis 3 right parenthesis vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line squared equals 37 plus 48 equals 85 space vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line equals square root of 85 

Jadi, vertical line u with rightwards arrow on top plus v with rightwards arrow on top vertical line equals square root of 85.

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

72

Muhammad Fadil

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Diketahui vektor-vektor a = 2 i − 3 j ​ , b = − 4 i − j ​ , dan c = − i + 2 j ​ . Nyatakan setiap vektor berikut kedalam vektor satuan i dan j ​ dan tentukan besarnya. b. 2 a + b − 3 c

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