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Diketahui panjang vektor dan panjang vektor . Jika sudut antara vektor dan vektor adalah . Nilai dari vektor

Pertanyaan

Diketahui panjang vektor a equals 4 dan panjang vektor b equals 6. Jika sudut antara vektor a dan vektor b adalah 120 degree. Nilai dari vektor a open parentheses a plus b close parentheses equals...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a with rightwards arrow on top close vertical bar end cell equals cell 4 comma space open vertical bar b with rightwards arrow on top close vertical bar equals 6 comma space theta equals 120 degree end cell row cell cos space theta end cell equals cell fraction numerator a with rightwards arrow on top. b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell cos space 120 degree end cell equals cell fraction numerator a with rightwards arrow on top. b with rightwards arrow on top over denominator 4 cross times 6 end fraction end cell row cell a with rightwards arrow on top. b with rightwards arrow on top end cell equals cell 24 space cos space 120 degree end cell row blank equals cell negative 12 end cell row cell a with rightwards arrow on top open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses end cell equals cell a with rightwards arrow on top squared plus stack a b with rightwards arrow on top end cell row cell a with rightwards arrow on top squared end cell equals cell a with rightwards arrow on top. a with rightwards arrow on top end cell row blank equals cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar space cos space theta end cell row blank equals cell 4 cross times 4 space cos space 0 end cell row blank equals cell 16 cross times 1 end cell row blank equals 16 row cell a with rightwards arrow on top open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses end cell equals cell a with rightwards arrow on top squared plus stack a b with rightwards arrow on top end cell row blank equals cell 16 plus open parentheses negative 12 close parentheses end cell row blank equals 4 end table

Jadi, nilai dari a with rightwards arrow on top open parentheses a with rightwards arrow on top plus b with rightwards arrow on top close parentheses equals 4.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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