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Jika a=[4,2,−3], b=[0,−1,5] dan c=[3,3,2].  a. Tentukan a+b−c

Pertanyaan

Jika begin mathsize 14px style straight a with rightwards arrow on top equals open square brackets 4 comma space 2 comma space minus 3 close square brackets end stylebegin mathsize 14px style straight b with rightwards arrow on top equals open square brackets 0 comma space minus 1 comma space 5 close square brackets end style dan begin mathsize 14px style c with rightwards arrow on top equals open square brackets 3 comma space 3 comma space 2 close square brackets end style

a. Tentukan begin mathsize 14px style a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top end style 

Pembahasan Soal:

Jika straight a with rightwards arrow on top equals open parentheses 4 comma space 2 comma space minus 3 close parenthesesstraight b with rightwards arrow on top equals open parentheses 0 comma space minus 1 comma space 5 close parentheses dan c with rightwards arrow on top equals open parentheses 3 comma space 3 comma space 2 close parentheses maka

table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus b with rightwards harpoon with barb upwards on top minus c with rightwards arrow on top end cell equals cell open parentheses 4 comma space 2 comma space minus 3 close parentheses plus open parentheses 0 comma negative 1 comma space 5 close parentheses minus open parentheses 3 comma space 3 comma space 2 close parentheses end cell row blank equals cell open parentheses 4 plus 0 minus 3 comma space 2 minus 1 minus 3 comma space minus 3 plus 5 minus 2 close parentheses end cell row blank equals cell open parentheses 1 comma space minus 2 comma space 0 close parentheses end cell end table 

Jadi hasilnya adalah a with rightwards arrow on top plus b with rightwards arrow on top minus c with rightwards arrow on top equals open parentheses 1 comma negative 2 comma 0 close parentheses.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Damanhuri

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

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Pembahasan Soal:

Ingat! Untuk sembarang titik straight P comma space straight Q comma space straight R maka berlaku penjumlahan vektor sebagai berikut:

top enclose PQ plus top enclose QR equals top enclose PR dan negative top enclose PQ equals top enclose QP

Perhatikan gambar kubus berikut ini!

Perhatikan bahwa top enclose SV equals top enclose PU sehingga dengan menggunakan konsep penjumlahan vektor diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose SV minus top enclose WU plus top enclose WQ end cell equals cell top enclose PU minus top enclose WU plus top enclose WQ end cell row blank equals cell top enclose PU minus open parentheses negative top enclose UW close parentheses plus top enclose WQ end cell row blank equals cell top enclose PU plus top enclose UW plus top enclose WQ end cell row blank equals cell top enclose PW plus top enclose WQ end cell row blank equals cell top enclose PQ end cell end table

Dengan demikian hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose SV end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose WU end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose WQ end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell top enclose PQ end cell end table.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

JIka vektor a=3i+5j​danb=4i−j​, vektor c yang memenuhi operasi 3b+2c=c−2a adalah ....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 straight b with rightwards arrow on top plus 2 straight c with rightwards arrow on top end cell equals cell straight c with rightwards arrow on top minus 2 straight a with rightwards arrow on top end cell row cell straight c with rightwards arrow on top end cell equals cell negative 3 straight b with rightwards arrow on top minus 2 straight a with rightwards arrow on top end cell row blank equals cell negative 3 left parenthesis 4 straight i with hat on top minus straight j with hat on top right parenthesis minus 2 left parenthesis 3 straight i with hat on top plus 5 straight j with hat on top right parenthesis end cell row blank equals cell negative 18 straight i with hat on top minus 7 straight j with hat on top end cell end table end style

Jadi, jawaban yang tepat adalah E.

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Roboguru

Diketahui : a=3i+4j+5kb=i+3kc=−2i+3j−4k  Nyatakan sebagai vektor kolom! e. a+(b+c)

Pembahasan Soal:

Pembahasan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses table row 3 row 4 row 5 end table close parentheses plus open parentheses table row 1 row 0 row 3 end table plus table row cell negative 2 end cell row 3 row cell negative 4 end cell end table close parentheses end cell row cell a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses table row 3 row 4 row 5 end table close parentheses plus open parentheses table row cell negative 1 end cell row 3 row cell negative 1 end cell end table close parentheses end cell row cell a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses table row 2 row 7 row 4 end table close parentheses end cell row cell a with rightwards arrow on top plus open parentheses b with rightwards arrow on top plus c with rightwards arrow on top close parentheses end cell equals cell open parentheses 2 i plus 7 j plus 4 k close parentheses end cell end table end style    

 

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Roboguru

Diketahui : a=3i+4j+5kb=i+3kc=−2i+3j−4k  Nyatakan sebagai vektor kolom! a. a+b

Pembahasan Soal:

Pembahasan:

begin mathsize 14px style a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses table row 3 row 4 row 5 end table close parentheses plus open parentheses table row 1 row 0 row 3 end table close parentheses equals open parentheses table row 4 row 4 row 8 end table close parentheses a with rightwards arrow on top plus b with rightwards arrow on top equals 4 i plus 4 j plus 8 k end style 

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Roboguru

Diketahui vektor p​=(42​) dan q​=(3−5​). Jika r=2p​−q​ dan s=2q​−3p​, hasil pengurangan r−s adalah ...

Pembahasan Soal:

Diketahui vektor begin mathsize 14px style straight p with rightwards arrow on top equals open parentheses table row 4 row 2 end table close parentheses end style dan begin mathsize 14px style straight q with rightwards arrow on top equals open parentheses table row 3 row cell negative 5 end cell end table close parentheses end style maka begin mathsize 14px style straight r with rightwards arrow on top equals 2 straight p with rightwards arrow on top minus straight q with rightwards arrow on top end style sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top end cell equals cell 2 p with rightwards arrow on top minus q with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row 4 row 2 end table close parentheses minus open parentheses table row 3 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 5 row 9 end table close parentheses end cell end table end style 

dan begin mathsize 14px style straight s with rightwards arrow on top equals 2 straight q with rightwards arrow on top minus 3 straight p with rightwards arrow on top end style diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell s with rightwards arrow on top end cell equals cell 2 q with rightwards arrow on top minus 3 p with rightwards arrow on top end cell row blank equals cell 2 open parentheses table row 3 row cell negative 5 end cell end table close parentheses minus 3 open parentheses table row 4 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell negative 6 end cell row cell negative 16 end cell end table close parentheses end cell end table end style 

sehingga hasil pengurangan begin mathsize 14px style straight r with rightwards arrow on top minus straight s with rightwards arrow on top end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell r with rightwards arrow on top minus s with rightwards arrow on top end cell equals cell open parentheses table row 5 row 9 end table close parentheses minus open parentheses table row cell negative 6 end cell row cell negative 16 end cell end table close parentheses end cell row blank equals cell open parentheses table row 11 row 25 end table close parentheses end cell end table end style 

Jadi, jawaban yang tepat adalah B.

 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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