Pertanyaan

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 $a = i + 2 j$ , $b = 3 i + j$ , dan $c = i + 9 j$ . Tentukan:

a. $a + b$

b. $∣ ∣ a + b ∣ ∣$

D. Kamilia

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

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

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 top , b 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.

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.

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 .