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b. Jika  dan , nyatakan dalam bentuk  setiap bentuk berikut. (i)   (ii)   (iii)

Pertanyaan

 

b. Jika begin mathsize 14px style PQ with rightwards arrow on top equals straight a with rightwards arrow on top end style dan begin mathsize 14px style PS with rightwards arrow on top equals straight b with rightwards arrow on top end style, nyatakan dalam bentuk begin mathsize 14px style straight a with rightwards arrow on top space dan space straight b with rightwards arrow on top end style setiap bentuk berikut.

(i) begin mathsize 14px style SR with rightwards arrow on top end style 

(ii) begin mathsize 14px style PR with rightwards arrow on top end style 

(iii) begin mathsize 14px style SQ with rightwards arrow on top end style 

Pembahasan Soal:

(i) begin mathsize 14px style SR with rightwards arrow on top equals PQ with rightwards arrow on top equals straight a with rightwards arrow on top end style  

(ii) begin mathsize 14px style PR with rightwards arrow on top end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PR with rightwards arrow on top end cell equals cell PQ with rightwards arrow on top plus QR with rightwards arrow on top end cell row blank equals cell PQ with rightwards arrow on top plus PS with rightwards arrow on top end cell row blank equals cell straight a with rightwards arrow on top plus straight b with rightwards arrow on top end cell end table end style 

(iii) begin mathsize 14px style SQ with rightwards arrow on top end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell SQ with rightwards arrow on top end cell equals cell SP with rightwards arrow on top plus PQ with rightwards arrow on top end cell row blank equals cell negative straight b with rightwards arrow on top plus straight a with rightwards arrow on top end cell row blank equals cell straight a with rightwards arrow on top minus straight b with rightwards arrow on top end cell end table end style 

Dengan demikian, hasil vektor yang ditanyakan adalah SR=aPR=a+b, dan SR=ab.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Indah

Mahasiswa/Alumni Universitas Diponegoro

Terakhir diupdate 13 September 2021

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Pertanyaan yang serupa

Perhatikan gambar !

Pembahasan Soal:

Diketahui :

begin mathsize 14px style u with rightwards arrow on top equals open square brackets table row 3 row 2 end table close square brackets end style

begin mathsize 14px style v with rightwards arrow on top equals open square brackets table row 6 row 8 end table close square brackets end style

begin mathsize 14px style w with rightwards arrow on top equals open square brackets table row 5 row 7 end table close square brackets end style 

Ditanya :

size 14px 2 size 14px u with size 14px rightwards arrow on top size 14px minus size 14px v with size 14px rightwards arrow on top size 14px plus size 14px 3 size 14px c with size 14px rightwards arrow on top size 14px equals size 14px. size 14px. size 14px. 

Jawab :

begin mathsize 14px style 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals 2 open square brackets table row 3 row 2 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus 3 open square brackets table row 5 row 7 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals 2 open square brackets table row 3 row 2 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus 3 open square brackets table row 5 row 7 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row 6 row 4 end table close square brackets minus open square brackets table row 6 row 8 end table close square brackets plus open square brackets table row 15 row 21 end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row cell 6 minus 6 plus 15 end cell row cell 4 minus 8 plus 21 end cell end table close square brackets 2 u with rightwards arrow on top minus v with rightwards arrow on top plus 3 w with rightwards arrow on top equals open square brackets table row 15 row 17 end table close square brackets end style 

0

Roboguru

Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan !

Pembahasan Soal:

vektor posisi dari titik A, B, dan C masing-masing sebagai berikut.

stack size 14px O size 14px A with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis 5 comma negative 3 right parenthesis end style stack size 14px O size 14px B with size 14px rightwards arrow on top size 14px equals size 14px b with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 2 comma negative 7 right parenthesis end style size 14px space stack size 14px O size 14px C with size 14px rightwards arrow on top size 14px equals size 14px c with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 6 comma 1 right parenthesis end style 

maka  begin mathsize 14px style AB with rightwards arrow on top comma space BC with rightwards arrow on top comma space end style dan begin mathsize 14px style AC with rightwards arrow on top end style

begin mathsize 14px style AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top space space space space space space equals left parenthesis negative 2 comma negative 7 right parenthesis minus left parenthesis 5 comma negative 3 right parenthesis space space space space space space equals left parenthesis negative 2 minus 5 comma negative 7 plus 3 right parenthesis space space space space space space equals left parenthesis negative 7 comma negative 4 right parenthesis BC with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top space space space space space space equals left parenthesis negative 6 comma 1 right parenthesis minus left parenthesis negative 2 comma negative 7 right parenthesis space space space space space space equals left parenthesis negative 6 plus 2 comma 1 plus 7 right parenthesis space space space space space space equals left parenthesis negative 4 comma 8 right parenthesis stack A C with rightwards arrow on top equals c with rightwards arrow on top minus a with rightwards arrow on top space space space space space equals open parentheses negative 6 comma 1 close parentheses minus open parentheses 5 comma negative 3 close parentheses space space space space space equals open parentheses negative 6 minus 5 comma 1 plus 3 close parentheses space space space space space equals open parentheses negative 11 comma 4 close parentheses end style  

Selanjutnya akan ditentukan  begin mathsize 14px style open parentheses AB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top end style

begin mathsize 14px style stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals left parenthesis negative 7 comma negative 4 right parenthesis plus left parenthesis negative 4 comma 8 right parenthesis space space space space space space space space space space space space space space equals left parenthesis negative 7 minus 4 comma negative 4 plus 8 right parenthesis space space space space space space space space space space space space space space equals left parenthesis negative 11 comma 4 right parenthesis open parentheses stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top equals left parenthesis negative 11 comma 4 right parenthesis plus open parentheses negative 11 comma 4 close parentheses space space space space space space space space space space space space space space space space space space space space space space space space equals open parentheses negative 22 comma 8 close parentheses end style 

Jadi, begin mathsize 14px style open parentheses AB with rightwards arrow on top plus BC with rightwards arrow on top close parentheses plus stack A C with rightwards arrow on top end style = begin mathsize 14px style open parentheses negative 22 comma 8 close parentheses end style 

0

Roboguru

Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan !

Pembahasan Soal:

vektor posisi dari titik A, B, dan C masing-masing sebagai berikut.

stack size 14px O size 14px A with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis 5 comma negative 3 right parenthesis end style stack size 14px O size 14px B with size 14px rightwards arrow on top size 14px equals size 14px b with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 2 comma negative 7 right parenthesis end style size 14px space stack size 14px O size 14px C with size 14px rightwards arrow on top size 14px equals size 14px c with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 6 comma 1 right parenthesis end style 

maka  begin mathsize 14px style AB with rightwards arrow on top end style dan begin mathsize 14px style BC with rightwards arrow on top end style

begin mathsize 14px style AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top space space space space space space equals open parentheses negative 2 comma negative 7 close parentheses minus open parentheses 5 comma negative 3 close parentheses space space space space space space equals open parentheses negative 2 minus 5 comma negative 7 plus 3 close parentheses space space space space space space equals open parentheses negative 7 comma negative 4 close parentheses BC with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top space space space space space space equals open parentheses negative 6 comma 1 close parentheses minus open parentheses negative 2 comma negative 7 close parentheses space space space space space space equals open parentheses negative 6 plus 2 comma 1 plus 7 close parentheses space space space space space space equals open parentheses negative 4 comma 8 close parentheses end style  

Selanjutnya akan ditentukan begin mathsize 14px style AB with rightwards arrow on top plus BC with rightwards arrow on top end style

begin mathsize 14px style stack A B with rightwards arrow on top plus stack B C with rightwards arrow on top equals open parentheses negative 7 comma negative 4 close parentheses plus open parentheses negative 4 comma 8 close parentheses space space space space space space space space space space space space space space equals open parentheses negative 7 minus 4 comma negative 4 plus 8 close parentheses space space space space space space space space space space space space space space equals open parentheses negative 11 comma 4 close parentheses end style 

Jadi, begin mathsize 14px style AB with rightwards arrow on top plus BC with rightwards arrow on top end style = begin mathsize 14px style left parenthesis negative 11 comma 4 right parenthesis end style 

0

Roboguru

Diketahui titik A(5,-3), B(-2,-7), dan C(-6,1). Tentukan  dan !

Pembahasan Soal:

vektor posisi dari titik A, B, dan C masing-masing sebagai berikut.

stack size 14px O size 14px A with size 14px rightwards arrow on top size 14px equals size 14px a with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis 5 comma negative 3 right parenthesis end style stack size 14px O size 14px B with size 14px rightwards arrow on top size 14px equals size 14px b with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 2 comma negative 7 right parenthesis end style size 14px space stack size 14px O size 14px C with size 14px rightwards arrow on top size 14px equals size 14px c with size 14px rightwards arrow on top size 14px equals begin mathsize 14px style left parenthesis negative 6 comma 1 right parenthesis end style 

maka  begin mathsize 14px style AB with rightwards arrow on top comma space BC with rightwards arrow on top comma space end style dan begin mathsize 14px style AC with rightwards arrow on top end style

begin mathsize 14px style AB with rightwards arrow on top equals b with rightwards arrow on top minus a with rightwards arrow on top space space space space space space equals left parenthesis negative 2 comma negative 7 right parenthesis minus left parenthesis 5 comma negative 3 right parenthesis space space space space space space equals left parenthesis negative 2 minus 5 comma negative 7 plus 3 right parenthesis space space space space space space equals left parenthesis negative 7 comma negative 4 right parenthesis BC with rightwards arrow on top equals c with rightwards arrow on top minus b with rightwards arrow on top space space space space space space equals left parenthesis negative 6 comma 1 right parenthesis minus left parenthesis negative 2 comma negative 7 right parenthesis space space space space space space equals left parenthesis negative 6 plus 2 comma 1 plus 7 right parenthesis space space space space space space equals left parenthesis negative 4 comma 8 right parenthesis stack A C with rightwards arrow on top equals c with rightwards arrow on top minus a with rightwards arrow on top space space space space space equals open parentheses negative 6 comma 1 close parentheses minus open parentheses 5 comma negative 3 close parentheses space space space space space equals open parentheses negative 6 minus 5 comma 1 plus 3 close parentheses space space space space space equals open parentheses negative 11 comma 4 close parentheses end style 

0

Roboguru

Pada gambar berikut E dan F berturut-turut titik tengah RS dan QS.    Jika  dan , nyatakan dalam  dan  untuk vektor-vektor : a.

Pembahasan Soal:

Penjumlahan vektor dengan menggunakan metode segitiga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell PS with rightwards arrow on top end cell equals cell PQ with rightwards arrow on top plus QS with rightwards arrow on top end cell row blank equals cell straight a with rightwards arrow on top plus QR with rightwards arrow on top plus RS with rightwards arrow on top end cell row blank equals cell straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top end cell end table end style 

Dengan demikian, jika dinyatakan dalam begin mathsize 14px style straight a with rightwards arrow on top comma straight b with rightwards arrow on top end style dan begin mathsize 14px style straight c with rightwards arrow on top end style maka vektor begin mathsize 14px style PS with rightwards arrow on top end style adalah PS=a+b+c.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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