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Diketahui vektor  dan . Tentukan panjang vektor .

Diketahui vektor begin mathsize 14px style a equals left parenthesis 4 comma negative 2 right parenthesis end style dan begin mathsize 14px style b equals open parentheses 5 comma 1 close parentheses end style. Tentukan panjang vektor begin mathsize 14px style open square brackets a plus b close square brackets end style.

Jawaban:

Vektor begin mathsize 14px style open square brackets a plus b close square brackets end style merupakan jumlah dua buah vektor, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus b end cell equals cell open parentheses 4 plus 5 comma space minus 2 plus 1 close parentheses end cell row blank equals cell open parentheses 9 comma space minus 1 close parentheses end cell end table end style

Ingat rumus panjang vektor, jika begin mathsize 14px style v left parenthesis x comma y right parenthesis rightwards arrow vertical line v vertical line equals square root of x squared plus y squared end root end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar a plus b close vertical bar end cell equals cell square root of 9 squared plus left parenthesis negative 1 right parenthesis squared end root end cell row blank equals cell square root of 81 plus 1 end root end cell row blank equals cell square root of 82 end cell end table end style

Jadi, panjang vektor begin mathsize 14px style a plus b equals square root of 82 end style.

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