Pertanyaan

Jika a = ( 3 − 1 ) dan b = ( − 2 4 ) , proyeksi skalar ( a − b ) pada ( 2 a + b ) adalah ....

Jika $a = (3 - 1)$ dan $b = (- 2 4)$ , proyeksi skalar $(a - b)$ pada $(2 a + b)$ adalah ....

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Diketahui dan , maka: Sehingga: Jadi, jawaban yang benar adalah D.

Diketahui straight a with rightwards arrow on top equals open parentheses table row 3 row cell negative 1 end cell end table close parentheses dan straight b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 4 end table close parentheses , maka:

Sehingga:

$open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses times open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses over denominator open vertical bar 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close vertical bar end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator open parentheses table row 5 row cell negative 5 end cell end table close parentheses times open parentheses table row 4 row 2 end table close parentheses over denominator 2 square root of 5 end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator 20 minus 10 over denominator 2 square root of 5 end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator 10 over denominator 2 square root of 5 end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator 5 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals fraction numerator 5 square root of 5 over denominator 5 end fraction open parentheses straight a with rightwards arrow on top minus straight b with rightwards arrow on top close parentheses subscript open parentheses 2 straight a with rightwards arrow on top plus straight b with rightwards arrow on top close parentheses end subscript equals square root of 5$

Jadi, jawaban yang benar adalah D.

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