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Diketahui vektor  dan vektor . Jika panjang vektor...

Diketahui vektor begin mathsize 14px style top enclose OP equals open parentheses table row 5 row straight x row 2 end table close parentheses end style dan vektor begin mathsize 14px style top enclose OQ equals open parentheses table row 7 row cell negative straight x end cell row 3 end table close parentheses end style. Jika panjang vektor begin mathsize 14px style top enclose PQ equals 3 end style dan begin mathsize 14px style straight x greater than 0 end style, nilai begin mathsize 14px style straight x end style adalah ....

  1. 5

  2.  4space space space space space space space space space space space space space space space

  3. 3space space space space space space space space space space space space space space space

  4. 2space space space space space space space space space space space space space space space

  5. 1space space space space space space space space space space space space space space space

Jawaban:

Diketahui :
vektor begin mathsize 14px style top enclose OP equals open parentheses table row 5 row straight x row 2 end table close parentheses end style 
ektor begin mathsize 14px style top enclose OQ equals open parentheses table row 7 row cell negative straight x end cell row 3 end table close parentheses end style
panjang vektor begin mathsize 14px style top enclose PQ equals 3 end style

begin mathsize 14px style straight x greater than 0 end style

Ditanya : nilai begin mathsize 14px style straight x end style adalah ....

Penyelesaian :

Rumus panjang vektor begin mathsize 14px style top enclose PQ end style diperoleh dari :

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open vertical bar top enclose PQ close vertical bar end cell equals cell square root of open parentheses straight x subscript straight Q minus straight x subscript straight P close parentheses squared plus open parentheses straight Y subscript straight Q minus straight Y subscript straight P close parentheses squared plus open parentheses straight Z subscript straight Q minus straight Z subscript straight P close parentheses squared end root end cell row 3 equals cell square root of open parentheses 7 minus 5 close parentheses squared plus open parentheses negative straight x minus straight x close parentheses squared plus open parentheses 3 minus 2 close parentheses squared end root end cell row 3 equals cell square root of 2 squared plus open parentheses negative 2 straight x close parentheses squared plus 1 squared end root end cell row 3 equals cell square root of 4 plus 4 straight x squared plus 1 end root end cell row 3 equals cell square root of 5 plus 4 straight x squared end root end cell row cell 3 squared end cell equals cell 5 plus 4 straight x squared end cell row cell 9 minus 5 end cell equals cell 4 straight x squared end cell row 4 equals cell 4 straight x squared end cell row 1 equals cell straight x squared end cell row straight x equals cell square root of 1 end cell row straight x equals cell plus-or-minus 1 end cell end table end style 
 

Karena begin mathsize 14px style straight x greater than 0 end style maka nilai begin mathsize 14px style straight x equals 1 end style 

Jadi, jawaban yang tepat adalah E

1

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