Pertanyaan

Diketahui vektor a ⇀ = ⎝ ⎛ − 2 3 4 ⎠ ⎞ d an b ⇀ = ⎝ ⎛ x 0 3 ⎠ ⎞ . Jika panjang proyeksi vektor a pada b adalah 5 4 , maka salah satu nilai x adalah ....

Diketahui vektor $a ⇀ = ⎝ ⎛ - 2 34 ⎠ ⎞ d an b ⇀ = ⎝ ⎛ x 03 ⎠ ⎞$ . Jika panjang proyeksi vektor a pada b adalah $\frac{4}{5}$ ,
maka salah satu nilai x adalah ....

6
4
2
-4
-6

R. RGFLSATU

Master Teacher

Jawaban terverifikasi

Pembahasan

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

Latihan Bab

Pengertian dan Operasi Vektor I

Operasi Vektor II

Kedudukan Vektor

Aljabar Vektor I