Pertanyaan

Tentukan a ⇀ ⋅ b ⇀ jika diketahui: b. a = 2 i − 8 j dan b = − 5 i − 2 j

Tentukan $a ⇀ \cdot b ⇀$ jika diketahui:

b. $a = 2 i - 8 j$ dan $b = - 5 i - 2 j$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

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table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell b with rightwards arrow on top end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table

Pembahasan

Ingat! Jika diketahui vektor dan maka Sehingga jikadiketahui Maka diperoleh a ⋅ b = = = = ( 2 i − 8 j ) ⋅ ( − 5 i − 2 j ) ( 2 ) ⋅ ( − 5 ) + ( − 8 ) ⋅ ( − 2 ) − 10 + 16 6 Dengan demikian, .

Ingat!

Jika diketahui vektor a with rightwards arrow on top equals a subscript 1 i with hat on top plus a subscript 2 j with hat on top dan b with rightwards arrow on top equals b subscript 1 i with hat on top plus b subscript 2 j with hat on top maka

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2

Sehingga jika diketahui

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top end cell equals cell 2 i with hat on top minus 8 j with hat on top end cell row cell b with rightwards arrow on top end cell equals cell negative 5 i with hat on top minus 2 j with hat on top end cell end table

Maka diperoleh

$a \cdot b = = = = (2 i - 8 j) \cdot (- 5 i - 2 j) (2) \cdot (- 5) + (- 8) \cdot (- 2) - 10 + 16 6$