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Diketahui vektor  dan . Besar sudut antara  adalah...

Diketahui vektor begin mathsize 14px style a equals left parenthesis 2 space comma negative 3 space comma 3 right parenthesis end style dan begin mathsize 14px style b equals left parenthesis 3 space comma negative 2 space comma negative 4 right parenthesis end style. Besar sudut antara undefined adalah ....
 

Jawaban:

Besar sudut antara dua vektor diperoleh dengan memanfaatkan rumus dot product undefined, dicari niliai cosinusnya terlebih dahulu.

Diketahui:

begin mathsize 14px style a equals open parentheses 2 comma negative 3 comma 3 close parentheses b equals left parenthesis 3 comma negative 2 comma negative 4 right parenthesis end style

Ditanya: sudut antara undefined?

Jawab:

Misal, undefinedsudut antara undefined.

Akan dicari nilai undefined terlebih dahulu.
 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space theta end cell equals cell fraction numerator a times b over denominator open vertical bar a close vertical bar open vertical bar b close vertical bar end fraction end cell row blank equals cell fraction numerator left parenthesis 2 times 3 right parenthesis plus left parenthesis left parenthesis negative 3 right parenthesis times left parenthesis negative 2 right parenthesis right parenthesis plus left parenthesis 3 times left parenthesis negative 4 right parenthesis right parenthesis over denominator square root of 2 squared plus left parenthesis negative 3 right parenthesis squared plus 3 to the power of 3 end exponent end root times square root of 3 squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root end fraction end cell row blank equals cell fraction numerator 6 plus 6 minus 12 over denominator square root of 4 plus 9 plus 9 end root times square root of 9 plus 4 plus 16 end root end fraction end cell row blank equals cell fraction numerator 0 over denominator square root of 22 times square root of 29 end fraction end cell row blank equals 0 end table end style
 

Didapat nilai begin mathsize 14px style cos space theta equals 0 end style, maka besar sudut begin mathsize 14px style theta end style adalah begin mathsize 14px style 90 degree end style.

Dengan demikian, besar sudut antara undefined adalah undefined.

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