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a=2i−2j​+k dan b=2i+3j​+6k, hitunglah besar sudut antara a dan b.

Pertanyaan

a with rightwards arrow on top equals 2 i with rightwards arrow on top minus 2 j with rightwards arrow on top plus k with rightwards arrow on top space dan space b equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 6 k with rightwards arrow on top, hitunglah besar sudut antara a with rightwards arrow on top space dan space b with rightwards arrow on top.

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

 besar sudut antara a with rightwards arrow on top space dan space b with rightwards arrow on top adalah 79.02 degree.

Pembahasan

Besar sudut antara a with rightwards arrow on top space dan space b with rightwards arrow on top didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell cos space alpha end cell equals cell fraction numerator open parentheses table row 2 row cell negative 2 end cell row 1 end table close parentheses times open parentheses table row 2 row 3 row 6 end table close parentheses over denominator square root of 2 squared plus open parentheses negative 2 close parentheses squared plus 1 squared end root space square root of 2 squared plus 3 squared plus 6 squared end root end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 4 plus open parentheses negative 6 close parentheses plus 6 over denominator square root of 9 space square root of 49 end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 4 over denominator open parentheses 3 close parentheses open parentheses 7 close parentheses end fraction end cell row cell cos space alpha end cell equals cell 4 over 21 end cell row alpha equals cell equals space 79.02 degree end cell end table  

Jadi, besar sudut antara a with rightwards arrow on top space dan space b with rightwards arrow on top adalah 79.02 degree.

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