Roboguru

Diketahui vektor dan vektor . Vektor satuan AB adalah ...

Diketahui vektor begin mathsize 14px style A equals i minus 2 j end style dan vektor begin mathsize 14px style B equals 4 i minus 5 j end style. Vektor satuan AB adalah ...

Jawaban:

begin mathsize 14px style misal space a with rightwards arrow on top equals a subscript 1 i plus a subscript 2 j space space rightwards arrow space vektor space satuan space dari space a with rightwards arrow on top equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction open vertical bar a with rightwards arrow on top close vertical bar equals square root of a subscript 1 superscript 2 plus a subscript 2 superscript 2 end root end stylebegin mathsize 14px style stack A B 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 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open vertical bar stack A B with rightwards arrow on top close vertical bar equals square root of 3 squared plus open parentheses negative 3 close parentheses squared end root space space space space space space equals open parentheses 4 i minus 5 j close parentheses minus open parentheses i minus 2 j 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 space space space space equals square root of 9 plus 9 end root space space space space space space equals 4 i minus 5 j minus i plus 2 j space space space space space space space space space 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 square root of 18 space space space space space space equals 3 i minus 3 j space space space space space space space space space space space space space space space space space space space space space 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 9 square root of 2   end style 

begin mathsize 14px style vektor space satuan space stack A B with rightwards arrow on top equals fraction numerator stack A B with rightwards arrow on top over denominator open vertical bar stack A B with rightwards arrow on top close vertical bar end fraction space space space space space 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 fraction numerator 3 i minus 3 j over denominator 9 square root of 2 end fraction space space space space space 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 1 over 18 square root of 2 open parentheses 3 i minus 3 j 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 space space space space space equals 1 over 6 square root of 2 i minus 1 over 6 square root of 2 j end style 

Jadi, vektor satuan begin mathsize 14px style stack A B with rightwards arrow on top equals 1 over 6 square root of 2 i minus 1 over 6 square root of 2 j end style.

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