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Pertanyaan

Vektor a = i + 4 j ​ − 4 k dan vektor b = 2 i + p j ​ − k . Jika a tegak lurus vektor b maka a + b = ....

Vektor  dan vektor . Jika  tegak lurus vektor  maka 

  1. begin mathsize 14px style 3 straight i with rightwards arrow on top minus 2 1 half straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style 

  2. begin mathsize 14px style 3 straight i with rightwards arrow on top plus 2 1 half straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style 

  3. begin mathsize 14px style 3 straight i with rightwards arrow on top plus 2 1 half straight j with rightwards arrow on top plus 5 straight k with rightwards arrow on top end style 

  4. begin mathsize 14px style negative 3 straight i with rightwards arrow on top plus 2 1 half straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style 

  5. begin mathsize 14px style negative 3 straight i with rightwards arrow on top minus 2 1 half straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

jawaban yang tepat adalah B.

Pembahasan

Vektor dan vektor . Jika tegak lurus vektor maka: Jadi didapat, atau dapat juga ditulis dalam bentuk . Dengan demikian, jawaban yang tepat adalah B.

Vektor begin mathsize 14px style straight a with rightwards arrow on top equals straight i with rightwards arrow on top plus 4 straight j with rightwards arrow on top minus 4 straight k with rightwards arrow on top end style dan vektor begin mathsize 14px style straight b with rightwards arrow on top equals 2 straight i with rightwards arrow on top plus straight p straight j with rightwards arrow on top minus straight k with rightwards arrow on top end style. Jika undefined tegak lurus vektor undefined maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top b with rightwards arrow on top end cell equals 0 row cell open parentheses table row 1 row 4 row cell negative 4 end cell end table close parentheses times space open parentheses table row 2 row p row cell negative 4 end cell end table close parentheses end cell equals 0 row cell 2 plus 4 p plus 4 end cell equals 0 row cell 4 p end cell equals cell negative 6 end cell row p equals cell negative 6 over 4 end cell row p equals cell negative 3 over 2 end cell end table end style 

Jadi didapat,

begin mathsize 14px style straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals open parentheses table row 1 row 4 row cell negative 4 end cell end table close parentheses plus open parentheses table row 2 row cell negative 3 over 2 end cell row cell negative 1 end cell end table close parentheses equals open parentheses table row 3 row cell 5 over 2 end cell row cell negative 5 end cell end table close parentheses end style  

atau dapat juga ditulis dalam bentuk begin mathsize 14px style straight a with rightwards arrow on top plus straight b with rightwards arrow on top equals 3 straight i with rightwards arrow on top plus 2 1 half straight j with rightwards arrow on top minus 5 straight k with rightwards arrow on top end style.

Dengan demikian, jawaban yang tepat adalah B.

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Diketahui vektor p ​ = 2 i − m j ​ + 3 k dan q ​ = 2 i − j ​ + m k saling tegak lurus, maka nilai m = ....

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