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Diketahui vektor-vektor a = i + 2 j ​ , b = 3 i + j ​ , dan c = i + 9 j ​ . Tentukan: a. a + b b. ∣ ∣ ​ a + b ∣ ∣ ​

Diketahui vektor-vektor , dan . Tentukan:

a. 

b. 

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D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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diperoleh dan .

diperoleh a with rightwards arrow on top plus b with rightwards arrow on top equals 4 i with rightwards arrow on top plus 3 j with rightwards arrow on top dan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals 5.

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Pembahasan

Gunakan konseppenjumlahan vektor dan panjang vektor. Diketahui vektor-vektor , , dan . a. Akan ditentukan vektor . Penjumlahan vektor secara aljabar dengan menjumlahkan unsur-unsur yang seletak. b. Akan ditentukan . Perhatikan perhitungan berikut. Jadi, diperoleh dan .

Gunakan konsep penjumlahan vektor dan panjang vektor.

m with rightwards arrow on top equals m subscript 1 i with rightwards arrow on top plus m subscript 2 j with rightwards arrow on top rightwards arrow open vertical bar m with rightwards arrow on top close vertical bar equals square root of open parentheses m subscript 1 close parentheses squared plus open parentheses m subscript 2 close parentheses squared end root

Diketahui vektor-vektor a with rightwards arrow on top equals i with rightwards arrow on top plus 2 j with rightwards arrow on topb with rightwards arrow on top equals 3 i with rightwards arrow on top plus j with rightwards arrow on top, dan c with rightwards arrow on top equals i with rightwards arrow on top plus 9 j with rightwards arrow on top.

a. Akan ditentukan vektor a with rightwards arrow on top plus b with rightwards arrow on top.

Penjumlahan vektor secara aljabar dengan menjumlahkan unsur-unsur yang seletak.

table attributes columnalign right center left columnspacing 2px end attributes row cell a with rightwards arrow on top plus b with rightwards arrow on top end cell equals cell open parentheses i with rightwards arrow on top plus 2 j with rightwards arrow on top close parentheses plus open parentheses 3 i with rightwards arrow on top plus j with rightwards arrow on top close parentheses end cell row blank equals cell open parentheses 1 plus 3 close parentheses i with rightwards arrow on top plus open parentheses 2 plus 1 close parentheses j with rightwards arrow on top end cell row blank equals cell 4 i with rightwards arrow on top plus 3 j with rightwards arrow on top end cell end table

b. Akan ditentukan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar end cell equals cell square root of open parentheses 4 close parentheses squared plus open parentheses 3 close parentheses squared end root end cell row blank equals cell square root of 16 plus 9 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 end table

Jadi, diperoleh a with rightwards arrow on top plus b with rightwards arrow on top equals 4 i with rightwards arrow on top plus 3 j with rightwards arrow on top dan open vertical bar a with rightwards arrow on top plus b with rightwards arrow on top close vertical bar equals 5.

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I

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