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Hitunglah besar sudut antara vektor a=3i+2j​+4k dan b=2i+3j​+3k.

Pertanyaan

Hitunglah besar sudut antara vektor a with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 4 k with rightwards arrow on top dan b with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 3 k with rightwards arrow on top.

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Jawaban

 besar sudut antara vektor a with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 4 k with rightwards arrow on top dan b with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 3 k with rightwards arrow on top. adalah 18 comma 20 degree

Pembahasan

Diketahui a with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 4 k with rightwards arrow on top dan b with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 3 k with rightwards arrow on top. Ingat bahwa cos space theta equals 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, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator open parentheses table row 3 row 2 row 4 end table close parentheses times open parentheses table row 2 row 3 row 3 end table close parentheses over denominator square root of 3 squared plus 2 squared plus 4 squared end root square root of 2 squared plus 3 squared plus 3 squared end root end fraction end cell row blank equals cell fraction numerator 3 times 2 plus 2 times 3 plus 4 times 3 over denominator square root of 9 plus 4 plus 16 end root square root of 4 plus 9 plus 9 end root end fraction end cell row blank equals cell fraction numerator 6 plus 6 plus 12 over denominator square root of 29 square root of 22 end fraction end cell row blank equals cell fraction numerator 24 over denominator square root of 638 end fraction end cell row blank almost equal to cell 0 comma 95 end cell row theta equals cell cos to the power of negative 1 end exponent open parentheses 0 comma 95 close parentheses end cell row blank equals cell 18 comma 20 degree end cell end table

Dengan demikian, besar sudut antara vektor a with rightwards arrow on top equals 3 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 4 k with rightwards arrow on top dan b with rightwards arrow on top equals 2 i with rightwards arrow on top plus 3 j with rightwards arrow on top plus 3 k with rightwards arrow on top. adalah 18 comma 20 degree

1rb+

4.5 (4 rating)

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Jawaban terverifikasi

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