tentukan besar sudut yang dibentuk oleh kedua vektor berikut. c. a=i dan b=j​

Pertanyaan

tentukan besar sudut yang dibentuk oleh kedua vektor berikut.

c. begin mathsize 14px style a with rightwards arrow on top equals i with rightwards arrow on top end style dan undefined 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

besar sudut antara begin mathsize 14px style a with rightwards arrow on top equals i with rightwards arrow on top end style dan undefined adalah begin mathsize 14px style 90 degree end style.

Pembahasan

Ingat kembali:

begin mathsize 14px style cos space theta equals fraction numerator a with rightwards arrow on top times b with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar times space open vertical bar b with rightwards arrow on top close vertical bar end fraction end style 

Maka:

begin mathsize 14px style a with rightwards arrow on top equals i with rightwards arrow on top space rightwards arrow space a with rightwards arrow on top equals open parentheses table row 1 row 0 end table close parentheses b with rightwards arrow on top equals j with rightwards arrow on top space rightwards arrow space b with rightwards arrow on top equals open parentheses table row 0 row 1 end table close parentheses end style 

Sehingga:

begin mathsize 14px style cos space theta equals fraction numerator a with rightwards arrow on top times space b with rightwards arrow on top over denominator stack open vertical bar a close vertical bar with rightwards arrow on top times space open vertical bar b with rightwards arrow on top close vertical bar end fraction cos space theta equals fraction numerator open parentheses table row 1 row 0 end table close parentheses times space open parentheses table row 0 row 1 end table close parentheses over denominator square root of 1 squared plus 0 squared end root times space square root of 0 squared plus 1 squared end root end fraction cos space theta equals fraction numerator 0 plus 0 over denominator square root of 1 plus 0 end root times space square root of 0 plus 1 end root end fraction cos space theta equals fraction numerator 0 over denominator 1 with rightwards arrow on top times space 1 end fraction cos space theta equals 0 over 1 cos space theta equals 0 cos space theta equals cos space 90 degree space space space space space space theta equals 90 degree end style  

Jadi, besar sudut antara begin mathsize 14px style a with rightwards arrow on top equals i with rightwards arrow on top end style dan undefined adalah begin mathsize 14px style 90 degree end style.

555

5.0 (1 rating)

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