Diketahui dan . Vektor proyeksi ortogonal pada v adalah adalah ....

Pertanyaan

Diketahui undefined dan . Vektor proyeksi ortogonal pada $\style{font-size:14px}{\overrightarrow{\mathrm v}}$ adalah adalah ....

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa

undefined

Misalkan vektor proyeksi ortogonal pada adalah . Oleh karena itu, didapatkan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses u with rightwards arrow on top plus v with rightwards arrow on top close parentheses ⋅ v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar squared end fraction close parentheses v with rightwards arrow on top end cell equals cell open parentheses fraction numerator open parentheses table row 0 row cell negative sign 9 end cell row 0 end table close parentheses ⋅ open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses over denominator open parentheses square root of 2 squared plus open parentheses negative sign 1 close parentheses squared plus open parentheses negative sign 2 close parentheses squared end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 ⋅ 2 plus open parentheses negative sign 9 close parentheses ⋅ open parentheses negative sign 1 close parentheses plus 0 ⋅ open parentheses negative sign 2 close parentheses over denominator open parentheses square root of 4 plus 1 plus 4 end root close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses fraction numerator 0 plus 9 plus 0 over denominator open parentheses square root of 9 close parentheses squared end fraction close parentheses open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 9 over 9 open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 2 row cell negative sign 1 end cell row cell negative sign 2 end cell end table close parentheses end cell row blank equals cell 2 i with rightwards arrow on top minus sign j with rightwards arrow on top minus sign 2 k with rightwards arrow on top end cell end table end style$

Jadi, jawaban yang tepat adalah C.