Proyeksi scalar orthogonal pada adalah . Nilai a...

Proyeksi scalar orthogonal $a with rightwards arrow on top equals open parentheses table row m row cell negative 6 end cell row cell negative 3 end cell end table close parentheses$ pada $b with rightwards arrow on top equals open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses$ adalah $1 1 third$ . Nilai $m$ adalah ...

Jawaban:

Misalkan proyeksi skalar orthogonal $a with rightwards arrow on top$ pada $b with rightwards arrow on top$ adalah $c with rightwards arrow on top$ . Ingat cara menentukan proyeksi skalar orthogonal yaitu $c with rightwards arrow on top equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction$ , sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar b with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 2 squared plus 1 squared plus left parenthesis negative 2 right parenthesis squared end root end cell row blank equals cell square root of 4 plus 1 plus 4 end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table$

maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell c with rightwards arrow on top end cell equals cell fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row cell 1 1 third end cell equals cell fraction numerator open parentheses table row m row cell negative 6 end cell row cell negative 3 end cell end table close parentheses times open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses over denominator 3 end fraction end cell row cell 4 over 3 cross times 3 end cell equals cell open parentheses table row m row cell negative 6 end cell row cell negative 3 end cell end table close parentheses times open parentheses table row 2 row 1 row cell negative 2 end cell end table close parentheses end cell row 4 equals cell 2 m minus 6 plus 6 end cell row 4 equals cell 2 m end cell row cell 4 over 2 end cell equals m row 2 equals m end table$

Jadi, dapat disimpulkan bahwa nilai $m$ adalah 2.

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