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Tentukan besar vektor berikut beserta vektor satua...

Tentukan besar vektor berikut beserta vektor satuannya.

a. begin mathsize 14px style v with rightwards arrow on top equals open parentheses table row 2 row 4 row 1 end table close parentheses end style

Jawaban:

Besar vektor begin mathsize 14px style v with rightwards arrow on top end style adalah sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open vertical bar v with rightwards arrow on top close vertical bar end cell equals cell square root of x squared plus y squared plus z squared end root end cell row blank equals cell square root of 2 squared plus 4 squared plus 1 squared end root end cell row blank equals cell square root of 4 plus 16 plus 1 end root end cell row blank equals cell square root of 21 end cell end table end style

Vektor satuan dari begin mathsize 14px style v with rightwards arrow on top end style dapat ditentukan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell v with hat on top end cell equals cell fraction numerator v with rightwards arrow on top over denominator open vertical bar v with rightwards arrow on top close vertical bar end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 21 end fraction open parentheses table row 2 row 4 row 1 end table close parentheses end cell row blank equals cell open parentheses table row cell 2 over 21 square root of 21 end cell row cell 4 over 21 square root of 21 end cell row cell 1 over 21 square root of 21 end cell end table close parentheses end cell end table end style

Dengan demikian vektor satuan dari undefined adalah begin mathsize 14px style v with hat on top equals open parentheses table row cell 2 over 21 square root of 21 end cell row cell 4 over 21 square root of 21 end cell row cell 1 over 21 square root of 21 end cell end table close parentheses end style

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