Pertanyaan

Diketahui koordinat A(-4,2,3), B(7,8,-1) dan C(1,0,7). Jika A B wakil vektor u , A C wakil vektor v , maka proyeksi pada adalah ....

Diketahui koordinat A(-4,2,3), B(7,8,-1) dan C(1,0,7). Jika $A B$ wakil vektor $u$ , $A C$ wakil vektor $v$ , maka proyeksi pada adalah ....

$3 square root of 5 i with rightwards arrow on top minus fraction numerator 6 over denominator square root of 5 end fraction j with rightwards arrow on top plus fraction numerator 12 over denominator square root of 5 end fraction k with rightwards arrow on top$

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Pembahasan

Diketahui koordinat A(-4,2,3), B(7,8,-1) dan C(1,0,7). Jika wakil vektor dan wakil , maka: Misal adalahproyeksi ortogonal vektor pada maka: atau

Diketahui koordinat A(-4,2,3), B(7,8,-1) dan C(1,0,7). Jika wakil vektor dan wakil , maka:

u with rightwards arrow on top equals stack A B with rightwards arrow on top equals B minus A equals open parentheses table row 7 row 8 row cell negative 1 end cell end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 row 3 end table close parentheses equals open parentheses table row 11 row 6 row cell negative 4 end cell end table close parentheses

v with rightwards arrow on top equals stack A C with rightwards arrow on top equals C minus A equals open parentheses table row 1 row 0 row 7 end table close parentheses minus open parentheses table row cell negative 4 end cell row 2 row 3 end table close parentheses equals open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses

Misal adalah proyeksi ortogonal vektor pada maka:

$z with rightwards arrow on top equals fraction numerator u with rightwards arrow on top. v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction. v with rightwards arrow on top$

$equals fraction numerator 11.5 plus 6. left parenthesis negative 2 right parenthesis plus left parenthesis negative 4 right parenthesis.4 over denominator open parentheses square root of 5 squared plus left parenthesis negative 2 right parenthesis squared plus 4 squared end root close parentheses squared end fraction space open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses$

equals 27 over 45 open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses

equals 3 over 5 open parentheses table row 5 row cell negative 2 end cell row 4 end table close parentheses

equals open parentheses table row 3 row cell negative 6 over 5 end cell row cell 12 over 5 end cell end table close parentheses

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