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Diketahui vektor-vektor berikut. a = ⎣ ⎡ ​ 1 2 3 ​ ⎦ ⎤ ​ , b = ⎣ ⎡ ​ − 5 3 − 2 ​ ⎦ ⎤ ​ , c = ⎣ ⎡ ​ 1 0 2 ​ ⎦ ⎤ ​ Proyeksi skalar a pada ( b + c ) adalah ...

Diketahui vektor-vektor berikut.

Proyeksi skalar  pada  adalah ...

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Jawaban terverifikasi

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proyeksi skalar pada adalah .

 proyeksi skalar straight a with rightwards arrow on top pada open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses adalah 2 over 5.

Pembahasan

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Tentukan terlebih dahulu. Proyeksiskalar pada Jadi,proyeksi skalar pada adalah .

Tentukan open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses terlebih dahulu.

table attributes columnalign right center left columnspacing 0px end attributes row cell straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell equals cell open square brackets table row cell negative 5 end cell row 3 row cell negative 2 end cell end table close square brackets plus open square brackets table row 1 row 0 row 2 end table close square brackets end cell row blank equals cell open square brackets table row cell negative 4 end cell row 3 row 0 end table close square brackets end cell end table

Proyeksi skalar straight a with rightwards arrow on top pada open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row straight s equals cell fraction numerator stack straight a times with rightwards arrow on top open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses over denominator open vertical bar open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses close vertical bar end fraction end cell row blank equals cell fraction numerator 1 open parentheses negative 4 close parentheses plus 2 open parentheses 3 close parentheses plus 3 open parentheses 0 close parentheses over denominator square root of open parentheses negative 4 close parentheses squared plus 3 squared plus 0 squared end root end fraction end cell row blank equals cell fraction numerator negative 4 plus 6 plus 0 over denominator square root of 16 plus 9 plus 0 end root end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 25 end fraction end cell row blank equals cell 2 over 5 end cell end table

Jadi, proyeksi skalar straight a with rightwards arrow on top pada open parentheses straight b with rightwards arrow on top plus straight c with rightwards arrow on top close parentheses adalah 2 over 5.

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