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Pertanyaan

Diketahui vektor a with rightwards harpoon with barb upwards on top equals open parentheses table row cell negative 2 end cell row 3 row 4 end table close parentheses space d a n space b with rightwards harpoon with barb upwards on top equals open parentheses table row x row 0 row 3 end table close parentheses. Jika panjang proyeksi vektor a pada b adalah 4 over 5,
maka salah satu nilai x adalah ....

  1. 6

  2. 4

  3. 2

  4. -4

  5. -6

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

V e k t o r space a equals open parentheses table row cell negative 2 end cell row 3 row 4 end table close parentheses space d a n space b equals space open parentheses table row x row 0 row 3 end table close parentheses space P a n j a n g space p r o y e k s i space v e k t o r stack space a with rightwards arrow on top space p a d a space b with rightwards arrow on top space a d a l a h space 4 over 5  fraction numerator a with rightwards arrow on top. b with rightwards arrow on top over denominator stack open vertical bar b close vertical bar with rightwards arrow on top end fraction equals 4 over 5  fraction numerator negative 2 x plus 10 plus 12 over denominator square root of x squared plus 0 plus 32 end root end fraction equals 4 over 5  fraction numerator negative 2 x plus 12 over denominator square root of x squared plus 9 end root end fraction equals 4 over 5  5 left parenthesis negative 2 x space plus space 12 right parenthesis space equals space 4 square root of x squared plus 9 end root  left parenthesis negative 10 x plus 60 right parenthesis space equals space 4 square root of x squared plus 9 end root  left parenthesis negative 10 x plus 60 right parenthesis squared space equals space left parenthesis 42 space right parenthesis left parenthesis x 2 space plus 9 right parenthesis squared  100 x squared space minus 1200 x space plus space 3600 space equals space 16 space left parenthesis x squared space plus space 9 right parenthesis  100 x squared space minus 1200 x space plus space 3600 space equals space 16 x squared space plus space 144  84 x squared space minus 1200 x space plus space 3456 space equals space 0  7 space x squared space minus space 100 x space plus space 288 space equals space 0  left parenthesis 7 x minus 72 right parenthesis left parenthesis x minus 4 right parenthesis equals 0  x space equals space 72 over 7 space a t a u space x space equals space 4

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Diketahui vektor a=3i+xj​+yk dengan panjang =14​ dan b=2i+3j​+6k. Jika panjang proyeksi vektor a pada vektor b sama dengan 3, maka nilai x+y= ...

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