Diketahui vektor u=⎝⎛​−443​⎠⎞​ dan v=⎝⎛​−3−60​⎠⎞​. Proyeksi vektor u pada v adalah....

Pertanyaan

Diketahui vektor u with rightwards arrow on top equals open parentheses table row cell negative 4 end cell row 4 row 3 end table close parentheses space d a n space v with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses. Proyeksi vektor u with rightwards arrow on top pada v with rightwards arrow on top adalah....

  1. 4 over 5 i minus 8 over 5 j

  2. negative 4 over 5 i minus 8 over 5 j

  3. 4 over 5 i plus 8 over 5 j

  4. 4 over 5 i minus 8 over 5 j plus 4 over 5 k

  5. negative 4 over 5 i minus 8 over 5 j plus 4 over 5 k

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

P r o y e k s i space v e k t o r space o r t h o g o n a l space u space ⃗ space p a d a space v space ⃑ comma space m i s a l k a n space c space ⃗  c with ⃗ on top equals fraction numerator u with ⃑ on top straight space. v with ⃑ on top over denominator open vertical bar v with ⃑ on top close vertical bar squared end fraction. v with ⃑ on top equals fraction numerator open parentheses table row cell negative 4 end cell row 4 row 3 end table close parentheses straight space. open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses over denominator open parentheses negative 3 close parentheses squared plus open parentheses negative 6 close parentheses squared plus open parentheses 0 close parentheses squared end fraction. open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses  equals fraction numerator open parentheses negative 4 close parentheses. open parentheses negative 3 close parentheses plus open parentheses 4 close parentheses. open parentheses negative 6 close parentheses plus 3 open parentheses 0 close parentheses over denominator 45 end fraction. open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses  equals fraction numerator negative 12 over denominator 45 end fraction open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses  c with ⃗ on top equals negative 4 over 15 open parentheses table row cell negative 3 end cell row cell negative 6 end cell row 0 end table close parentheses equals open parentheses table row cell 4 over 5 end cell row cell 8 over 5 end cell row 0 end table close parentheses space a t a u space space c with ⃗ on top equals 4 over 5 i plus 8 over 5 j plus 0 k

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Diketahui vektor a=⎝⎛​−4−22​⎠⎞​ dan b=⎝⎛​5−14​⎠⎞​. Proyeksi orthogonal vektor a pada vektor b adalah ...

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