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Pertanyaan

Tentukan besar sudut yang terbentuk pada vektor a = 2 i + 1 j − 3 k dan vektor b = − 1 i + 3 j − 2 k !

Tentukan besar sudut yang terbentuk pada vektor dan vektor !

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D. Enty

Master Teacher

Jawaban terverifikasi

Jawaban

besar sudut antara kedua vektor tersebut adalah .

besar sudut antara kedua vektor tersebut adalah 60 degree.

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Pembahasan

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Menentukan Menentukan Menentukan Menentukan besar sudut Jadi, besar sudut antara kedua vektor tersebut adalah .

Menentukan bold a with bold rightwards arrow on top bold times bold b with bold rightwards arrow on top

table attributes columnalign right center left columnspacing 0px end attributes row cell bold a with bold rightwards arrow on top bold times bold b with bold rightwards arrow on top end cell equals cell left parenthesis 2 cross times left parenthesis negative 1 right parenthesis right parenthesis plus left parenthesis 1 cross times 3 right parenthesis plus left parenthesis left parenthesis negative 3 right parenthesis cross times left parenthesis negative 2 right parenthesis right parenthesis end cell row blank equals cell negative 2 plus 3 plus 6 end cell row blank equals 7 end table 

Menentukan bold vertical line bold a with bold rightwards arrow on top bold vertical line

table attributes columnalign right center left columnspacing 0px end attributes row cell bold vertical line bold a with bold rightwards arrow on top bold vertical line end cell equals cell square root of 2 squared plus 1 squared plus left parenthesis negative 3 right parenthesis squared end root end cell row blank equals cell square root of 4 plus 1 plus 9 end root end cell row blank equals cell square root of 14 end cell end table 

Menentukan bold vertical line bold b with bold rightwards arrow on top bold vertical line

table attributes columnalign right center left columnspacing 0px end attributes row cell bold vertical line bold b with bold rightwards arrow on top bold vertical line end cell equals cell square root of left parenthesis negative 1 right parenthesis squared plus 3 squared plus left parenthesis negative 2 right parenthesis squared end root end cell row blank equals cell square root of 1 plus 9 plus 4 end root end cell row blank equals cell square root of 14 end cell end table 

Menentukan besar sudut

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space alpha end cell equals cell fraction numerator bold a with bold rightwards arrow on top bold times bold b with bold rightwards arrow on top over denominator bold vertical line bold a with bold rightwards arrow on top bold vertical line bold vertical line bold b with bold rightwards arrow on top bold vertical line end fraction end cell row cell cos space alpha end cell equals cell fraction numerator 7 over denominator square root of 14 times square root of 14 end fraction end cell row cell cos space alpha end cell equals cell 7 over 14 end cell row cell cos space alpha end cell equals cell 1 half end cell row alpha equals cell cos to the power of negative 1 end exponent open parentheses 1 half close parentheses end cell row alpha equals cell 60 degree end cell end table 

Jadi, besar sudut antara kedua vektor tersebut adalah 60 degree.

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Diketahui vektor u = ⎝ ⎛ ​ 2 − 1 1 ​ ⎠ ⎞ ​ dan v → = ⎝ ⎛ ​ 7 0 1 ​ ⎠ ⎞ ​ . Tentukan sudut antara u dan v .

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