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Pertanyaan

Jika sudut antara vektor stack text a end text with rightwards arrow on top equals 7 stack text i end text with rightwards arrow on top plus square root of p stack text j end text with rightwards arrow on top plus 4 stack text k end text with rightwards arrow on top dan vektor stack text b end text with rightwards arrow on top equals 4 stack text i end text with rightwards arrow on top plus square root of p stack text j end text with rightwards arrow on top minus 2 stack text k end text with rightwards arrow on top adalah 45 degree, maka text p end text sama dengan ...

  1. 5 

  2. 20 

  3. 25 

  4. 35 

  5. 36 

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Panjang vektor a with rightwards arrow on top equals x i with rightwards arrow on top plus y j with rightwards arrow on top plus z k with rightwards arrow on top, yaitu open vertical bar a with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root

Jika vektor a with rightwards arrow on top equals a subscript 1 i with rightwards arrow on top plus a subscript 2 j with rightwards arrow on top plus a subscript 3 k with rightwards arrow on top dan b with rightwards arrow on top equals b subscript 1 i with rightwards arrow on top plus b subscript 2 j with rightwards arrow on top plus b subscript 3 k with rightwards arrow on top, maka

a with rightwards arrow on top times b with rightwards arrow on top equals a subscript 1 times b subscript 1 plus a subscript 2 times b subscript 2 plus a subscript 3 times b subscript 3

Jika vektor a with rightwards arrow on top dan b with rightwards arrow on top membentuk sudut alpha, maka 

a with rightwards arrow on top times b with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space cos space alpha

Panjang vektor a with rightwards arrow on top dan b with rightwards arrow on top pada soal di atas adalah sebagai berikut.

open vertical bar a with rightwards arrow on top close vertical bar equals square root of 7 squared plus open parentheses square root of p close parentheses squared plus 4 squared end root equals square root of p plus 65 end root

open vertical bar b with rightwards arrow on top close vertical bar equals square root of 4 squared plus open parentheses square root of p close parentheses squared plus open parentheses negative 2 close parentheses squared end root equals square root of p plus 20 end root

Hasil perkalian vektor a with rightwards arrow on top dan b with rightwards arrow on top adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open parentheses table row 7 row cell square root of p end cell row 4 end table close parentheses open parentheses table row 4 row cell square root of p end cell row cell negative 2 end cell end table close parentheses end cell row blank equals cell 7 times 4 plus square root of p times square root of p plus 4 times open parentheses negative 2 close parentheses end cell row blank equals cell 28 plus p minus 8 end cell row blank equals cell p plus 20 end cell end table

Nilai p dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top times b with rightwards arrow on top end cell equals cell open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar space cos space alpha end cell row cell p plus 20 end cell equals cell square root of p plus 65 end root times square root of p plus 20 end root times cos space 45 degree end cell row cell p plus 20 end cell equals cell square root of open parentheses p plus 65 close parentheses open parentheses p plus 20 close parentheses end root times 1 half square root of 2 end cell row cell 2 p plus 40 end cell equals cell square root of p squared plus 85 p plus 1300 end root times square root of 2 end cell row cell 4 p squared plus 160 p plus 1600 end cell equals cell 2 open parentheses p squared plus 85 p plus 1300 close parentheses end cell row cell 2 p squared plus 80 p plus 800 end cell equals cell p squared plus 85 p plus 1300 end cell row cell p squared minus 5 p minus 500 end cell equals 0 row cell open parentheses p plus 20 close parentheses open parentheses p minus 25 close parentheses end cell equals 0 end table

p equals negative 20 space text atau end text space p equals 25

Oleh karena itu, jawaban yang tepat adalah C.

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