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Diketahui titik A(3, 2, −1), B(2, 1, 0)  dan C(−1, 2, 3). Jika AB⇀ wakil dari vektor u⇀ dan AC⇀ wakil dari vektor v⇀. Maka proyeksi vektor pada adalah...

Pertanyaan

Diketahui titik A left parenthesis 3 comma space 2 comma space minus 1 right parenthesis comma space B left parenthesis 2 comma space 1 comma space 0 right parenthesis  dan C left parenthesis negative 1 comma space 2 comma space 3 right parenthesis. Jika stack A B with rightwards harpoon with barb upwards on top wakil dari vektor u with rightwards harpoon with barb upwards on top dan stack A C with rightwards harpoon with barb upwards on top wakil dari vektor v with rightwards harpoon with barb upwards on top. Maka proyeksi vektor u with rightwards harpoon with barb upwards on top pada v with rightwards harpoon with barb upwards on top adalah...

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

proyeksi vektor u with rightwards harpoon with barb upwards on top pada v with rightwards harpoon with barb upwards on top adalah open parentheses negative 1 comma space 0 comma space 1 close parentheses equals negative i plus k.

Pembahasan

table attributes columnalign right center left columnspacing 0px end attributes row cell u with rightwards harpoon with barb upwards on top end cell equals cell stack A B with rightwards harpoon with barb upwards on top end cell row blank equals cell B minus A end cell row blank equals cell open parentheses table row 2 row 1 row 0 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell negative 1 end cell row 1 end table close parentheses end cell row cell v with rightwards harpoon with barb upwards on top end cell equals cell stack A C with rightwards harpoon with barb upwards on top end cell row blank equals cell C minus A end cell row blank equals cell open parentheses table row cell negative 1 end cell row 2 row 3 end table close parentheses minus open parentheses table row 3 row 2 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses end cell end table

Menentukan proyeksi vektor u with rightwards harpoon with barb upwards on top pada v with rightwards harpoon with barb upwards on top

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator u with rightwards harpoon with barb upwards on top cross times v with rightwards harpoon with barb upwards on top over denominator open vertical bar v with rightwards harpoon with barb upwards on top close vertical bar squared end fraction cross times v with rightwards harpoon with barb upwards on top end cell equals cell fraction numerator open parentheses table row cell negative 1 end cell row cell negative 1 end cell row 1 end table close parentheses cross times open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses over denominator open vertical bar open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses close vertical bar squared end fraction cross times open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses end cell row blank equals cell fraction numerator 4 plus 0 plus 4 over denominator open parentheses square root of open parentheses negative 4 close parentheses squared plus 0 squared plus 4 squared end root close parentheses squared end fraction cross times open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses end cell row blank equals cell fraction numerator 8 over denominator 16 plus 16 end fraction cross times open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses end cell row blank equals cell 8 over 32 cross times open parentheses table row cell negative 4 end cell row 0 row 4 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row 0 row 1 end table close parentheses end cell row blank equals cell negative i plus k end cell end table

Jadi, proyeksi vektor u with rightwards harpoon with barb upwards on top pada v with rightwards harpoon with barb upwards on top adalah open parentheses negative 1 comma space 0 comma space 1 close parentheses equals negative i plus k.

1rb+

5.0 (3 rating)

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