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Diketahui vektor-vektor berikut : a = ⎝ ⎛ ​ 1 1 2 ​ ​ ⎠ ⎞ ​ b = ⎝ ⎛ ​ 2 2 2 ​ p ​ ⎠ ⎞ ​ c = ⎝ ⎛ ​ 0 q 2 ​ ​ ⎠ ⎞ ​ Jika panjang proyeksi skalar vektor b pada vektor a adalah 1, dan vektor tegak lurus dengan vektor c , maka nilai p + q adalah…

Diketahui vektor-vektor berikut :

 

Jika panjang proyeksi skalar vektor  pada vektor  adalah 1, dan vektor begin mathsize 14px style straight b with rightwards arrow on top end style tegak lurus dengan vektor , maka nilai p + q adalah…

  1. -1

  2. 0

  3. 1

  4. 2

  5. 3

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 begin mathsize 14px style straight p plus straight q equals negative 2 plus 1 equals negative 1 end style

Pembahasan

Panjang proyeksi skalar vektor pada vektor adalah 1, berarti : Jadi

Panjang proyeksi skalar vektor begin mathsize 14px style straight b with rightwards arrow on top end style pada vektor begin mathsize 14px style straight a with rightwards arrow on top end style adalah 1, berarti :

begin mathsize 14px style fraction numerator straight b with rightwards arrow on top. straight a with rightwards arrow on top over denominator open vertical bar straight a with rightwards arrow on top close vertical bar end fraction equals 1 fraction numerator open parentheses table row 2 row cell 2 square root of 2 end cell row straight p end table close parentheses space. space open parentheses table row 1 row 1 row cell square root of 2 end cell end table close parentheses over denominator square root of 1 squared plus open parentheses 1 close parentheses squared plus open parentheses square root of 2 close parentheses squared end root end fraction equals 1 fraction numerator 2 plus 2 square root of 2 plus straight p square root of 2 over denominator 2 end fraction equals 1 2 plus 2 square root of 2 plus straight p square root of 2 equals 2 straight p square root of 2 equals negative 2 square root of 2 straight p equals negative 2  straight b with rightwards arrow on top perpendicular straight c with rightwards arrow on top left right double arrow straight b with rightwards arrow on top space. space straight c with rightwards arrow on top equals 0 open parentheses table row 2 row cell 2 square root of 2 end cell row cell negative 2 end cell end table close parentheses space. space open parentheses table row 0 row straight q row cell square root of 2 end cell end table close parentheses equals 0 2 square root of 2 straight q minus 2 square root of 2 equals 0 2 square root of 2 straight q equals 2 square root of 2 straight q equals 1 end style 

Jadi begin mathsize 14px style straight p plus straight q equals negative 2 plus 1 equals negative 1 end style

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