Diketahui vektor m=(815​) dan vektor n=(3p​). ∣∣​m∣∣​+∣∣​n∣∣​=22. Tentukan nilai p.

Pertanyaan

Diketahui vektor begin mathsize 14px style m with rightwards arrow on top equals open parentheses table row 8 row 15 end table close parentheses end style dan vektor begin mathsize 14px style n with rightwards arrow on top equals open parentheses table row 3 row p end table close parentheses end style. begin mathsize 14px style open vertical bar m with rightwards arrow on top close vertical bar plus open vertical bar n with rightwards arrow on top close vertical bar equals 22 end style. Tentukan nilai p.

A. Arifianto

Master Teacher

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Jawaban

nilai p yang mungkin adalah begin mathsize 14px style 4 space atau space minus 4 end style.

Pembahasan

Ingat rumus panjang vektor pada dua dimensi adalah sebagai berikut.

x with rightwards arrow on top equals open parentheses table row a row b end table close parentheses rightwards arrow open vertical bar x with rightwards arrow on top close vertical bar equals square root of a squared plus b squared end root.

Diketahui vektor begin mathsize 14px style m with rightwards arrow on top equals open parentheses table row 8 row 15 end table close parentheses end style dan vektor begin mathsize 14px style n with rightwards arrow on top equals open parentheses table row 3 row p end table close parentheses end style. Soal di atas dapat kita selesaikan seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line m with rightwards arrow on top vertical line plus vertical line n with rightwards arrow on top vertical line end cell equals 22 row cell square root of 8 squared plus 15 squared end root plus square root of 3 squared plus p squared end root end cell equals 22 row cell square root of 289 plus square root of 3 squared plus p squared end root end cell equals 22 row cell 17 plus square root of 9 plus p squared end root end cell equals 22 row cell square root of 9 plus p squared end root end cell equals cell 22 minus 17 end cell row cell square root of 9 plus p squared end root end cell equals 5 row cell 9 plus p squared end cell equals 25 row cell p squared end cell equals cell 25 minus 9 end cell row cell p squared end cell equals 16 row p equals cell plus-or-minus square root of 16 end cell row p equals cell plus-or-minus 4 end cell end table 

Jadi, nilai p yang mungkin adalah begin mathsize 14px style 4 space atau space minus 4 end style.

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