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Diketahui vektor a = 2 i − p j ​ + 3 k dan b = i − 2 j ​ + 2 k . Jika | c | adalah panjang proyeksi vektor a pada b , dan | | = 4,maka nilai p adalah....

Diketahui vektor dan . Jika || adalah panjang proyeksi vektor pada, dan |begin mathsize 14px style c with rightwards arrow on top end style| = 4,maka nilai p adalah....

  1. -4

  2. -2

  3. 2

  4. 4

  5. 8

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S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

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Pembahasan

open vertical bar straight c with rightwards arrow on top close vertical bar equals 4  open vertical bar fraction numerator straight a with rightwards arrow on top times straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar end fraction close vertical bar equals 4  open vertical bar fraction numerator open parentheses table row 2 row cell negative straight p end cell row 3 end table close parentheses times open parentheses table row 1 row cell negative 2 end cell row 2 end table close parentheses over denominator square root of 1 squared plus open parentheses negative 2 close parentheses squared plus 2 squared end root end fraction close vertical bar equals 4  open vertical bar fraction numerator 2 plus 2 straight p plus 6 over denominator 3 end fraction close vertical bar equals 4  fraction numerator 2 plus 2 straight p plus 6 over denominator 3 end fraction equals 4 space atau space fraction numerator 2 plus 2 straight p plus 6 over denominator 3 end fraction equals negative 4  2 plus 2 straight p plus 6 equals 12 space space space space space space space space space space 2 plus 2 straight p plus 6 equals negative 12  2 straight p plus 8 equals 12 space space space space space space space space space space space space space space space space space 2 straight p plus 8 equals negative 12  2 straight p equals 4 space space space space space space space space space space space space space space space space space space space space space space space space space space 2 straight p equals negative 20  bold p bold equals bold 2 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space space space space space space space space space space space space space space space straight p equals negative 10

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