Pertanyaan

Diketahui vektor u = ⎝ ⎛ 0 2 2 ⎠ ⎞ dan v = ⎝ ⎛ − 2 0 2 ⎠ ⎞ . Proyeksi vektor orthogonal u pada v adalah....

Diketahui vektor $u = ⎝ ⎛ 022 ⎠ ⎞$ dan $v = ⎝ ⎛ - 2 02 ⎠ ⎞ .$ Proyeksi vektor orthogonal $u$ pada $v$ adalah....

-i + k
-i - k
-2i + k
2i - k

F. Pratama

Master Teacher

Mahasiswa/Alumni Universitas Putra Indonesia YPTK Padang

Jawaban terverifikasi

Pembahasan

$Proyeksi space vektor space orthogonal space straight u with rightwards arrow on top space pada space straight v with rightwards arrow on top space adalah space fraction numerator straight u with rightwards arrow on top. straight v with rightwards arrow on top over denominator open vertical bar straight v with rightwards arrow on top close vertical bar squared end fraction. straight v with rightwards arrow on top Jadi comma space proyeksi space orthogonal space vektor space straight a with rightwards arrow on top equals open parentheses table row 0 row 2 row 2 end table close parentheses space pada space vektor space straight b with rightwards arrow on top equals open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses fraction numerator straight a with rightwards arrow on top. straight b with rightwards arrow on top over denominator open vertical bar straight b with rightwards arrow on top close vertical bar squared end fraction. straight b with rightwards arrow on top equals fraction numerator open parentheses table row 0 row 2 row 2 end table close parentheses. straight space open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses over denominator open parentheses square root of left parenthesis negative 2 right parenthesis squared plus 0 squared plus open parentheses 2 close parentheses squared end root close parentheses squared end fraction. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses equals 4 over 8. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses equals 1 half. open parentheses table row cell negative 2 end cell row 0 row 2 end table close parentheses equals 1 half open parentheses negative 2 straight i with rightwards arrow on top plus 2 straight k with rightwards arrow on top close parentheses equals negative straight i with rightwards arrow on top plus straight k with rightwards arrow on top$