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Diketahui kubus ABCD.EFGH dengan titik A(3, 0, 0), C(0, 7​, 0), D(0, 0, 0), F(3, 7​, 4), dan H(0, 0, 4). Sudut antara vektor DH dan DF adalah ....

Pertanyaan

Diketahui kubus ABCD. EFGH dengan titik straight A open parentheses 3 comma space 0 comma space 0 close parenthesesstraight C open parentheses 0 comma space square root of 7 comma space 0 close parenthesesstraight D open parentheses 0 comma space 0 comma space 0 close parenthesesstraight F open parentheses 3 comma space square root of 7 comma space 4 close parentheses, dan straight H open parentheses 0 comma space 0 comma space 4 close parentheses. Sudut antara vektor DH with rightwards arrow on top dan DF with rightwards arrow on top adalah ....

  1. 15 degree

  2. 30 degree

  3. 45 degree

  4. 60 degree

  5. 90 degree

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah C.

Diketahui kubus ABCD. EFGH dengan titik straight A open parentheses 3 comma space 0 comma space 0 close parenthesesstraight C open parentheses 0 comma space square root of 7 comma space 0 close parenthesesstraight D open parentheses 0 comma space 0 comma space 0 close parenthesesstraight F open parentheses 3 comma space square root of 7 comma space 4 close parentheses, dan straight H open parentheses 0 comma space 0 comma space 4 close parentheses, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell DH with rightwards arrow on top end cell equals cell straight H minus straight D end cell row blank equals cell open parentheses table row 0 row 0 row 4 end table close parentheses minus open parentheses table row 0 row 0 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 0 row 0 row 4 end table close parentheses end cell row cell DF with rightwards arrow on top end cell equals cell straight F minus straight D end cell row blank equals cell open parentheses table row 3 row cell square root of 7 end cell row 4 end table close parentheses minus open parentheses table row 0 row 0 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell square root of 7 end cell row 4 end table close parentheses end cell end table

Ingat bahwa, table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta end cell equals cell fraction numerator DH with rightwards arrow on top times DF with rightwards arrow on top over denominator open vertical bar DH with rightwards arrow on top close vertical bar times open vertical bar DF with rightwards arrow on top close vertical bar end fraction end cell end table, maka

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight theta end cell equals cell fraction numerator DH with rightwards arrow on top times DF with rightwards arrow on top over denominator open vertical bar DH with rightwards arrow on top close vertical bar times open vertical bar DF with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row 0 row 0 row 4 end table close parentheses times open parentheses table row 3 row cell square root of 7 end cell row 4 end table close parentheses over denominator square root of 0 squared plus 0 squared plus 4 squared end root square root of 3 squared plus square root of 7 squared plus 4 squared end root end fraction end cell row blank equals cell fraction numerator 0 plus 0 plus 16 over denominator square root of 16 square root of 32 end fraction end cell row blank equals cell fraction numerator 16 over denominator 16 square root of 2 end fraction end cell row blank equals cell 1 half square root of 2 end cell row blank equals cell cos space 45 degree end cell row straight theta equals cell 45 degree end cell end table

Oleh karena itu, jawaban yang benar adalah C.

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