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Pertanyaan

Jika P(2,1,2), A(9,-6,2), dan B(2,-4,7), maka sudut antara PA dan PB adalah ....

Jika P(2,1,2), A(9,-6,2), dan B(2,-4,7), maka sudut antara  dan  adalah ....

  1. 30°

  2.   45°

  3. 60°

  4. 90°

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A. Acfreelance

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Jawaban terverifikasi

Pembahasan

Sehingga Maka

begin mathsize 14px style PA with rightwards arrow on top equals open parentheses table row 9 row cell negative 6 end cell row 2 end table close parentheses minus open parentheses table row 2 row 1 row 2 end table close parentheses equals open parentheses table row 7 row cell negative 7 end cell row 0 end table close parentheses PB with rightwards arrow on top equals open parentheses table row 2 row cell negative 4 end cell row 7 end table close parentheses minus open parentheses table row 2 row 1 row 2 end table close parentheses equals open parentheses table row 0 row cell negative 5 end cell row 5 end table close parentheses end style 

Sehingga

begin mathsize 14px style PA with rightwards arrow on top space. space PB with rightwards arrow on top equals open parentheses table row 7 row cell negative 7 end cell row 0 end table close parentheses space. space open parentheses table row 0 row cell negative 5 end cell row 5 end table close parentheses equals 0 plus 35 plus 0 equals 35 open vertical bar PA with rightwards arrow on top close vertical bar equals square root of 7 squared plus open parentheses negative 7 close parentheses squared plus 0 squared end root equals square root of 49 plus 49 plus 0 end root equals square root of 98 equals 7 square root of 2 open vertical bar PB with rightwards arrow on top close vertical bar equals square root of 0 squared plus open parentheses negative 5 close parentheses squared plus 5 squared end root equals square root of 0 plus 25 plus 25 end root equals square root of 50 equals 5 square root of 2 end style 

Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta end cell equals cell fraction numerator PA with rightwards arrow on top space. space PB with rightwards arrow on top over denominator open vertical bar PA with rightwards arrow on top close vertical bar space. space open vertical bar PB with rightwards arrow on top close vertical bar end fraction end cell row cell cos space straight theta end cell equals cell fraction numerator 35 over denominator open parentheses 7 square root of 2 close parentheses open parentheses 5 square root of 2 close parentheses end fraction end cell row cell cos space straight theta end cell equals cell 35 over 70 end cell row cell cos space straight theta end cell equals cell 1 half end cell row straight theta equals cell 60 degree end cell end table end style 

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Diketahui titik A(1, 0, –2), B(2, 1, –1), C(2, 0, –3). Sudut antara vektor AB dengan AC adalah ….

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