Pertanyaan

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

Diketahui titik $A (3, 2, - 1), B (2, 1, 0)$ dan $C (- 1, 2, 3)$ . Jika $A B ⇀$ wakil dari vektor $u ⇀$ dan $A C ⇀$ wakil dari vektor $v ⇀$ . 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 pada adalah .

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

Menentukan proyeksi vektor pada Jadi, proyeksi vektor pada adalah .

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 .