Roboguru

Diketahui  Panjang vektor  adalah...

Pertanyaan

Diketahui open vertical bar top enclose a close vertical bar equals square root of 3 comma space open vertical bar top enclose b close vertical bar equals 1 space d a n space open vertical bar top enclose a minus top enclose b close vertical bar equals 1. Panjang vektor top enclose a plus top enclose b adalah...

  1. square root of 3

  2. square root of 5

  3. square root of 7

  4. 2 square root of 2

  5. 3

Pembahasan Soal:

Diketahui :

Diketahui open vertical bar top enclose a close vertical bar equals square root of 3 comma space open vertical bar top enclose b close vertical bar equals 1 space d a n space open vertical bar top enclose a minus top enclose b close vertical bar equals 1. 

DItanya :

Panjang vektor top enclose a plus top enclose b adalah...

Penyelesaian :

Akan  cari terlebih dahulu a.b dari perpangkatan vertical line a space minus space b vertical line

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line a space minus space b vertical line squared space end cell equals cell space a squared minus 2 a b plus b squared end cell row cell 1 squared space end cell equals cell space square root of 3 squared minus space 2 a b plus 1 squared end root space end cell end table

untukspace a squared equals space vertical line a vertical line squared danspace b squared equals vertical line b vertical line untukspace a. b space equals space vertical line a vertical line. vertical line b vertical line. cos space alpha,

karena tidak memiliki sudut α (sudut antara vektor a dan vektor b),maka tidak dapat dicari dengan cara dot vektor

table attributes columnalign right center left columnspacing 0px end attributes row cell space 1 space end cell equals cell space 3 space minus space 2 ab space plus space 1 space space space space end cell row cell 2 ab space space end cell equals cell space 3 space plus space 1 space minus space 1 space space space end cell row cell space 2 ab space space end cell equals cell space 3 space space space space end cell row cell space ab space space space end cell equals cell 3 over 2 end cell end table

Selanjutnyta pangkatkan vertical line a space plus space b vertical line


table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight a space plus space straight b vertical line ² space end cell equals cell space straight a ² space plus space 2 ab space plus space straight b ² space end cell row cell vertical line straight a space plus space straight b vertical line ² space end cell equals cell space 3 ² space plus space 2. open parentheses 3 over 2 close parentheses space plus space 1 ² space end cell row cell vertical line straight a space plus space straight b vertical line ² space end cell equals cell space 3 space plus space 3 space plus space 1 space end cell row cell vertical line straight a space plus space straight b vertical line ² space end cell equals cell space 7 space end cell row cell vertical line straight a space plus space straight b vertical line space end cell equals cell space 7 end cell end table
 

Jadi, nilai dari vertical line a space plus space b vertical line space equals space square root of 7.

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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